- At what time did the trip begin? Give the answer in 12-hour format.
- What was Reggie's average speed for the remaining 35 km of the trip in km/h?
Notice (8): Undefined variable: tuMain [APP/Controller/Component/CommonComponent.php, line 4554]Code Context}
}
if($tuMain > $mauMain && $tuMain%$mauMain != 0)
$clone = array( 'id' => '15402', 'chart' => '', 'question_id' => '44163', 'clone_type' => '1', 'phpfile' => null, 'clone_symbol' => null, 'clone_content' => '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>', 'clone_solution_step' => '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h', 'clone_answer' => '(a) 0$(t8) $(m10); (b) $(n20) km/h ', 'array' => object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} }, 'clone_image' => null, 'clone_solution_step_image' => null, 'clone_answer_image' => null, 'status' => true, 'created' => '2019-09-08 23:34:33', 'modified' => '2019-09-09 10:39:12', 'original_question' => 'Kenny and Jerry started on a 50-kim cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 40 km, Kenny cycled faster than Jerry. He arrived at the fining point 40 minutes before Jerry who was 10 km behind him. Jerry did not change his speed throughout and completed it at 11 30. <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was Kenny's average speed for the remaining 40 km of the trip in km/h?</li> </ol>', 'formula' => array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ), 'time_value' => array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ), 'criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'type_criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'image_gridline' => '', 'code_gridline' => '', 'level' => '', 'topic_id' => '', 'source' => '', 'question_code' => 'P6.SP.JC.19090801-A1', 'tag' => '', 'mark' => '', 'text_working' => '["","","","","","","","","","","","","","","\/\/","","","","","","","","","","","$(n40) \u00f7 $(h2) = $(n20)","","","",""]', 'original_solution' => '(a)<br /> Jerry's average speed<br /> = 10 ÷ <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 15 km/h<br /> <br /> Time that Jerry took for the trip<br /> = 50 ÷ 15<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h<br /> <br /> 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h before 11 30 is 08 10.<br /> <br /> (b)<br /> Time that Kenny took for the remaining 40 km of the trip<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 2 h<br /> <br /> Kenny's average speed<br /> = 40 ÷ 2<br /> = 20 km/h<br /> <br /> Answer(s): (a) 08 10; (b) 20 km/h', 'delete_by' => null, 'delete_date' => null ) $Array1 = object(Array1) { table => 'array1s' validate => array() useDbConfig => 'default' useTable => 'array1s' id => '61' data => array() schemaName => 'ischoolb_orgi' primaryKey => 'id' validationErrors => array() validationDomain => null tablePrefix => '' plugin => null name => 'Array1' alias => 'Array1' tableToModel => array( 'array1s' => 'Array1' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => array( 'id' => array( [maximum depth reached] ), 'name' => array( [maximum depth reached] ), 'content' => array( [maximum depth reached] ), 'note' => array( [maximum depth reached] ), 'created' => array( [maximum depth reached] ), 'modified' => array( [maximum depth reached] ) ) [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => true [protected] _eventManager => object(CakeEventManager) {} [protected] _validator => null } $Prime = object(AppModel) { useDbConfig => 'default' useTable => 'primes' id => false data => array() schemaName => null table => 'primes' primaryKey => 'id' validate => array() validationErrors => array() validationDomain => null plugin => null name => 'Prime' alias => 'Prime' tableToModel => array( 'primes' => 'Prime' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => null [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => false [protected] _eventManager => null [protected] _validator => null } $answer_fix = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $count_crition = (int) 51 $count_array_break = (int) 0 $count_variable_nnt = (int) 0 $message_nnt = '' $field = 'time_value' $array_get = array( (int) 0 => 'n10', (int) 8 => 'n50', (int) 9 => 'n50', (int) 6 => 'n10', (int) 2 => 't40', (int) 14 => 'h11', (int) 18 => 'm30', (int) 1 => '(n40)', (int) 25 => '(n40)', (int) 3 => '(t60)', (int) 4 => '(st60)', (int) 5 => '(st60)', (int) 22 => '(st60)', (int) 7 => '(n15)', (int) 10 => '(n15)', (int) 28 => '(n15)', (int) 20 => '(h3)', (int) 21 => '(h3)', (int) 11 => '(z)', (int) 12 => '(sz)', (int) 13 => '(sz)', (int) 15 => '(t1)', (int) 16 => '(w)', (int) 17 => '(w)', (int) 19 => '(m10)' ) $tempt = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $list_name_array = array( (int) 0 => 'Julian', (int) 1 => 'Brandon' ) $list_array_item = array( 'Jerry' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 5, 'manyArray' => '1', 'capitalize' => '0' ), 'Kenny' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 12, 'manyArray' => '1', 'capitalize' => '0' ) ) $list_italic = array() $array_variable = object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} } $question_content = '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>' $solution_step = '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h' $clone_answer = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $formula = array( (int) 0 => '45-15=30', (int) 1 => 'if(more_than(30>20))continue', (int) 2 => 'print_fraction(6,60)=6/60', (int) 3 => 'simplify_fraction(6/60)=1/10', (int) 4 => 'get_numerator(1/10)=1', (int) 5 => 'get_denominator(1/10)=10', (int) 6 => '15/1*10=150', (int) 7 => 'if(whole_number(150))continue', (int) 8 => 'get_quotient(45,150)=0', (int) 9 => 'get_remainder(45,150)=45', (int) 10 => 'print_fraction(45,150)=45/150', (int) 11 => 'simplify_fraction(45/150)=3/10', (int) 12 => 'get_numerator(3/10)=3', (int) 13 => 'get_denominator(3/10)=10', (int) 14 => '7-0=7', (int) 15 => '3/10*60=18', (int) 16 => 'if(more_than(18>9))continue', (int) 17 => 'if(whole_number(18))continue', (int) 18 => '30-18=12', (int) 19 => 'if(more_than(12>9))continue', (int) 20 => 'do_fraction(+:0,3/10)=$(hw)', (int) 21 => 'if(more_than(0>0))continue', (int) 22 => 'do_fraction(+:1/10,1/10)=$(2sz)', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2)', (int) 24 => 'if(more_than($(h2)>1))continue', (int) 25 => 'do_fraction(/:30,$(h2))=$(n20s)', (int) 26 => 'simplify_fraction($(n20s))=$(n20)', (int) 27 => 'if(more_than($(n20)>35))back', (int) 28 => 'if(more_than($(n20)>150))continue', (int) 29 => '' ) $formula_1 = array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ) $criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $type_criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $time_value = array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ) $k = '1567995994231' $v = object(stdClass) { cate => 'items' name => 'Kenny' range => '61' attr => object(stdClass) {} } $array_system = array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ) $dem_array_trung = (int) 1 $value_rand_check = (int) 12 $value_check = 'Brandon' $tempt_array = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $tempt_k = (int) 4 $tempt_v = '30' $check_who_nnt = (int) 0 $from = '7' $to = '9' $findme = '/' $arr_variable = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon', '(n40)' => (int) 30, '(t60)' => '6/60', '(st60)' => '1/10', '(tt2)' => (int) 1, '(tt3)' => (int) 10, '(n15)' => (int) 150, '(h3)' => '0', '(r3)' => '45', '(z)' => '45/150', '(sz)' => '3/10', '(t1)' => (int) 3, '(t3)' => (int) 10, '(t8)' => (int) 7, '(w)' => (float) 18, '(m10)' => (int) 12 ) $variable_k = '(m10)' $variable_v = '12' $formula_k = (int) 20 $formula_v = 'do_fraction(+:$(h3),$(sz))=$(hw)' $criterion_k = (int) 29 $criterion_v = '' $type_criterion_k = (int) 29 $type_criterion_v = '' $variable_show = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon' ) $start = 'do_fraction(' $end = ')' $array_mixed_nnt = array() $check_changes = '' $criterion_continue = '))=$(hw)' $criterion_back = '(hw)' $type_criterion_action = (int) 1 $get_between = '+:0,3/10' $type_cri = 'more_than' $get_between_value = '12>9' $bieuthuc = array( (int) 0 => 'do_fraction(+:0,3/10)', (int) 1 => '(hw)' ) $substr_pos = 'change_decimal_to_fraction' $get_numerator = false $get_whole_number_nnt = false $pos = false $giatri = '' $substr_simplify_frac = 'simplify_fraction' $simplify_frac = false $substr_simplify_ratio = 'simplify_ratio' $simplify_ratio = false $substr_get_element_of_ratio = 'get_element' $get_element_of_ratio = false $substr_numberto2decimal = 'change_number_to_2dp' $change_to_2dp = false $substr_digit_5_0 = 'change_to_2dp_with_5_or_0' $change_to_2dp_5_or_0 = false $substr_mixed_num = 'change_improper_to_mixed_number' $mixed_num = false $substr_mixed_to_improper = 'change_mixed_number_to_improper' $mixed_to_improper = false $substr_invert_fraction = 'invert_fraction' $invert_fraction = false $substr_get_same_numerator = 'share_same_numerator' $get_same_numerator = false $substr_get_same_denominator = 'share_same_denominator' $get_same_denominator = false $substr_reduce_into_ratio = 'simplify_any_into_ratio' $reduce_into_ratio = false $substr_multiply_subscript = 'multiply_ratio_subscript' $multiply_subscript = false $substr_assign = 'assign' $assign = false $substr_is_12_hour_time_am_pm = 'get_12_hour_time_am_pm' $is_12_hour_time_am_pm = false $substr_is_2400_hour_time = 'get_2400_hour_time' $is_2400_hour_time = false $substr_add_or_minus_time = 'add_or_minus_min_or_s' $add_or_minus_time = false $substr_change_percentage_to_frac = 'change_percentage_to_frac' $change_percentage_to_frac = false $substr_round_2_decimal = 'round_2_decimal_place' $round_2_decimal_place = false $substr_round_1_decimal = 'round_1_decimal_place' $round_1_decimal_place = false $substr_get_quotient = 'get_quotient' $get_quotient = false $substr_get_remainder = 'get_remainder' $get_remainder = false $substr_change_min_to_hour_min = 'change_min_to_h_min' $change_min_to_hour_min = false $substr_change_h_min_to_min = 'change_h_min_to_min' $change_h_min_to_min = false $substr_carry_1 = 'carry_1_from_mixed_number' $get_carry_1 = false $change_d_or_p_to_fraction = 'change_to_unsimplied_fraction' $get_change_d_or_p_to_fraction = false $round_off_to_nearest_ten = 'round_off_to_nearest_ten' $get_round_off_to_nearest_ten = false $round_off_to_nearest_hundred = 'round_off_to_nearest_hundred' $get_round_off_to_nearest_hundred = false $round_off_to_nearest_thousand = 'round_off_to_nearest_thousand' $get_round_off_to_nearest_thousand = false $change_12_to_24 = 'change_12h_to_24h' $get_12_to_24 = false $change_24_to_12 = 'change_24h_to_12h' $get_24_to_12 = false $get_factors = 'get_factors' $get_factors_nnt = false $get_common_factors = 'get_common_factors' $get_common_factors_nnt = false $get_multiples = 'get_multiples' $get_multiples_23916 = false $get_add_or_minus_multiples = 'add_or_minus_multiples' $add_or_minus_multiples_23916 = false $get_common_numbers = 'get_common_numbers' $get_common_numbers_240916 = false $substr_array_singular = 'array_singular' $array_singular_101016 = false $substr_array_plural = 'array_plural' $array_plural_101016 = false $substr_print_fraction = 'print_fraction' $print_fraction_101016 = false $substr_array_capitalize = 'array_capitalize' $array_capitalize_101016 = false $substr_array_get_words = 'array_get_words' $array_get_words_31316 = false $substr_array_get_1st_letter = 'array_get_1st_letter' $array_array_get_1st_letter = false $substr_array_get_next_loop = 'array_get_next_loop' $array_get_next_loop = false $substr_array_get_next_break = 'array_get_next_break' $array_get_next_break = false $substr_multiply_fraction = 'do_fraction' $array_multiply_fraction = (int) 0 $substr_change_to_italic = 'change_to_italic' $array_change_to_italic = false $match = array( (int) 0 => 'print_fraction(45,150)', (int) 1 => '45,150', (int) 2 => ')' ) $count_check = array( (int) 0 => '+', (int) 1 => '0,3/10' ) $arr_caculoid = array( (int) 0 => '+', (int) 1 => '-', (int) 2 => '*', (int) 3 => '/' ) $two_fraction = array( (int) 0 => '0', (int) 1 => '3/10' ) $findme2 = '.' $search_tu = false $search_tu2 = false $search_mau = (int) 1 $search_mau2 = false $tuOne = '0' $mauOne = (int) 1 $split_mau = array( (int) 0 => '3', (int) 1 => '10' ) $tuTwo = '3' $mauTwo = '10' $k1 = (int) 29 $v1 = ''CommonComponent::generateAdvClone() - APP/Controller/Component/CommonComponent.php, line 4554 ClonesController::index2() - APP/Controller/ClonesController.php, line 2226 ReflectionMethod::invokeArgs() - [internal], line ?? Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167 [main] - APP/webroot/index.php, line 119
Notice (8): Undefined variable: mauMain [APP/Controller/Component/CommonComponent.php, line 4554]Code Context}
}
if($tuMain > $mauMain && $tuMain%$mauMain != 0)
$clone = array( 'id' => '15402', 'chart' => '', 'question_id' => '44163', 'clone_type' => '1', 'phpfile' => null, 'clone_symbol' => null, 'clone_content' => '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>', 'clone_solution_step' => '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h', 'clone_answer' => '(a) 0$(t8) $(m10); (b) $(n20) km/h ', 'array' => object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} }, 'clone_image' => null, 'clone_solution_step_image' => null, 'clone_answer_image' => null, 'status' => true, 'created' => '2019-09-08 23:34:33', 'modified' => '2019-09-09 10:39:12', 'original_question' => 'Kenny and Jerry started on a 50-kim cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 40 km, Kenny cycled faster than Jerry. He arrived at the fining point 40 minutes before Jerry who was 10 km behind him. Jerry did not change his speed throughout and completed it at 11 30. <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was Kenny's average speed for the remaining 40 km of the trip in km/h?</li> </ol>', 'formula' => array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ), 'time_value' => array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ), 'criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'type_criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'image_gridline' => '', 'code_gridline' => '', 'level' => '', 'topic_id' => '', 'source' => '', 'question_code' => 'P6.SP.JC.19090801-A1', 'tag' => '', 'mark' => '', 'text_working' => '["","","","","","","","","","","","","","","\/\/","","","","","","","","","","","$(n40) \u00f7 $(h2) = $(n20)","","","",""]', 'original_solution' => '(a)<br /> Jerry's average speed<br /> = 10 ÷ <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 15 km/h<br /> <br /> Time that Jerry took for the trip<br /> = 50 ÷ 15<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h<br /> <br /> 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h before 11 30 is 08 10.<br /> <br /> (b)<br /> Time that Kenny took for the remaining 40 km of the trip<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 2 h<br /> <br /> Kenny's average speed<br /> = 40 ÷ 2<br /> = 20 km/h<br /> <br /> Answer(s): (a) 08 10; (b) 20 km/h', 'delete_by' => null, 'delete_date' => null ) $Array1 = object(Array1) { table => 'array1s' validate => array() useDbConfig => 'default' useTable => 'array1s' id => '61' data => array() schemaName => 'ischoolb_orgi' primaryKey => 'id' validationErrors => array() validationDomain => null tablePrefix => '' plugin => null name => 'Array1' alias => 'Array1' tableToModel => array( 'array1s' => 'Array1' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => array( 'id' => array( [maximum depth reached] ), 'name' => array( [maximum depth reached] ), 'content' => array( [maximum depth reached] ), 'note' => array( [maximum depth reached] ), 'created' => array( [maximum depth reached] ), 'modified' => array( [maximum depth reached] ) ) [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => true [protected] _eventManager => object(CakeEventManager) {} [protected] _validator => null } $Prime = object(AppModel) { useDbConfig => 'default' useTable => 'primes' id => false data => array() schemaName => null table => 'primes' primaryKey => 'id' validate => array() validationErrors => array() validationDomain => null plugin => null name => 'Prime' alias => 'Prime' tableToModel => array( 'primes' => 'Prime' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => null [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => false [protected] _eventManager => null [protected] _validator => null } $answer_fix = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $count_crition = (int) 51 $count_array_break = (int) 0 $count_variable_nnt = (int) 0 $message_nnt = '' $field = 'time_value' $array_get = array( (int) 0 => 'n10', (int) 8 => 'n50', (int) 9 => 'n50', (int) 6 => 'n10', (int) 2 => 't40', (int) 14 => 'h11', (int) 18 => 'm30', (int) 1 => '(n40)', (int) 25 => '(n40)', (int) 3 => '(t60)', (int) 4 => '(st60)', (int) 5 => '(st60)', (int) 22 => '(st60)', (int) 7 => '(n15)', (int) 10 => '(n15)', (int) 28 => '(n15)', (int) 20 => '(h3)', (int) 21 => '(h3)', (int) 11 => '(z)', (int) 12 => '(sz)', (int) 13 => '(sz)', (int) 15 => '(t1)', (int) 16 => '(w)', (int) 17 => '(w)', (int) 19 => '(m10)' ) $tempt = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $list_name_array = array( (int) 0 => 'Julian', (int) 1 => 'Brandon' ) $list_array_item = array( 'Jerry' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 5, 'manyArray' => '1', 'capitalize' => '0' ), 'Kenny' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 12, 'manyArray' => '1', 'capitalize' => '0' ) ) $list_italic = array() $array_variable = object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} } $question_content = '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>' $solution_step = '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h' $clone_answer = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $formula = array( (int) 0 => '45-15=30', (int) 1 => 'if(more_than(30>20))continue', (int) 2 => 'print_fraction(6,60)=6/60', (int) 3 => 'simplify_fraction(6/60)=1/10', (int) 4 => 'get_numerator(1/10)=1', (int) 5 => 'get_denominator(1/10)=10', (int) 6 => '15/1*10=150', (int) 7 => 'if(whole_number(150))continue', (int) 8 => 'get_quotient(45,150)=0', (int) 9 => 'get_remainder(45,150)=45', (int) 10 => 'print_fraction(45,150)=45/150', (int) 11 => 'simplify_fraction(45/150)=3/10', (int) 12 => 'get_numerator(3/10)=3', (int) 13 => 'get_denominator(3/10)=10', (int) 14 => '7-0=7', (int) 15 => '3/10*60=18', (int) 16 => 'if(more_than(18>9))continue', (int) 17 => 'if(whole_number(18))continue', (int) 18 => '30-18=12', (int) 19 => 'if(more_than(12>9))continue', (int) 20 => 'do_fraction(+:0,3/10)=$(hw)', (int) 21 => 'if(more_than(0>0))continue', (int) 22 => 'do_fraction(+:1/10,1/10)=$(2sz)', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2)', (int) 24 => 'if(more_than($(h2)>1))continue', (int) 25 => 'do_fraction(/:30,$(h2))=$(n20s)', (int) 26 => 'simplify_fraction($(n20s))=$(n20)', (int) 27 => 'if(more_than($(n20)>35))back', (int) 28 => 'if(more_than($(n20)>150))continue', (int) 29 => '' ) $formula_1 = array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ) $criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $type_criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $time_value = array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ) $k = '1567995994231' $v = object(stdClass) { cate => 'items' name => 'Kenny' range => '61' attr => object(stdClass) {} } $array_system = array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ) $dem_array_trung = (int) 1 $value_rand_check = (int) 12 $value_check = 'Brandon' $tempt_array = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $tempt_k = (int) 4 $tempt_v = '30' $check_who_nnt = (int) 0 $from = '7' $to = '9' $findme = '/' $arr_variable = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon', '(n40)' => (int) 30, '(t60)' => '6/60', '(st60)' => '1/10', '(tt2)' => (int) 1, '(tt3)' => (int) 10, '(n15)' => (int) 150, '(h3)' => '0', '(r3)' => '45', '(z)' => '45/150', '(sz)' => '3/10', '(t1)' => (int) 3, '(t3)' => (int) 10, '(t8)' => (int) 7, '(w)' => (float) 18, '(m10)' => (int) 12 ) $variable_k = '(m10)' $variable_v = '12' $formula_k = (int) 20 $formula_v = 'do_fraction(+:$(h3),$(sz))=$(hw)' $criterion_k = (int) 29 $criterion_v = '' $type_criterion_k = (int) 29 $type_criterion_v = '' $variable_show = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon' ) $start = 'do_fraction(' $end = ')' $array_mixed_nnt = array() $check_changes = '' $criterion_continue = '))=$(hw)' $criterion_back = '(hw)' $type_criterion_action = (int) 1 $get_between = '+:0,3/10' $type_cri = 'more_than' $get_between_value = '12>9' $bieuthuc = array( (int) 0 => 'do_fraction(+:0,3/10)', (int) 1 => '(hw)' ) $substr_pos = 'change_decimal_to_fraction' $get_numerator = false $get_whole_number_nnt = false $pos = false $giatri = '' $substr_simplify_frac = 'simplify_fraction' $simplify_frac = false $substr_simplify_ratio = 'simplify_ratio' $simplify_ratio = false $substr_get_element_of_ratio = 'get_element' $get_element_of_ratio = false $substr_numberto2decimal = 'change_number_to_2dp' $change_to_2dp = false $substr_digit_5_0 = 'change_to_2dp_with_5_or_0' $change_to_2dp_5_or_0 = false $substr_mixed_num = 'change_improper_to_mixed_number' $mixed_num = false $substr_mixed_to_improper = 'change_mixed_number_to_improper' $mixed_to_improper = false $substr_invert_fraction = 'invert_fraction' $invert_fraction = false $substr_get_same_numerator = 'share_same_numerator' $get_same_numerator = false $substr_get_same_denominator = 'share_same_denominator' $get_same_denominator = false $substr_reduce_into_ratio = 'simplify_any_into_ratio' $reduce_into_ratio = false $substr_multiply_subscript = 'multiply_ratio_subscript' $multiply_subscript = false $substr_assign = 'assign' $assign = false $substr_is_12_hour_time_am_pm = 'get_12_hour_time_am_pm' $is_12_hour_time_am_pm = false $substr_is_2400_hour_time = 'get_2400_hour_time' $is_2400_hour_time = false $substr_add_or_minus_time = 'add_or_minus_min_or_s' $add_or_minus_time = false $substr_change_percentage_to_frac = 'change_percentage_to_frac' $change_percentage_to_frac = false $substr_round_2_decimal = 'round_2_decimal_place' $round_2_decimal_place = false $substr_round_1_decimal = 'round_1_decimal_place' $round_1_decimal_place = false $substr_get_quotient = 'get_quotient' $get_quotient = false $substr_get_remainder = 'get_remainder' $get_remainder = false $substr_change_min_to_hour_min = 'change_min_to_h_min' $change_min_to_hour_min = false $substr_change_h_min_to_min = 'change_h_min_to_min' $change_h_min_to_min = false $substr_carry_1 = 'carry_1_from_mixed_number' $get_carry_1 = false $change_d_or_p_to_fraction = 'change_to_unsimplied_fraction' $get_change_d_or_p_to_fraction = false $round_off_to_nearest_ten = 'round_off_to_nearest_ten' $get_round_off_to_nearest_ten = false $round_off_to_nearest_hundred = 'round_off_to_nearest_hundred' $get_round_off_to_nearest_hundred = false $round_off_to_nearest_thousand = 'round_off_to_nearest_thousand' $get_round_off_to_nearest_thousand = false $change_12_to_24 = 'change_12h_to_24h' $get_12_to_24 = false $change_24_to_12 = 'change_24h_to_12h' $get_24_to_12 = false $get_factors = 'get_factors' $get_factors_nnt = false $get_common_factors = 'get_common_factors' $get_common_factors_nnt = false $get_multiples = 'get_multiples' $get_multiples_23916 = false $get_add_or_minus_multiples = 'add_or_minus_multiples' $add_or_minus_multiples_23916 = false $get_common_numbers = 'get_common_numbers' $get_common_numbers_240916 = false $substr_array_singular = 'array_singular' $array_singular_101016 = false $substr_array_plural = 'array_plural' $array_plural_101016 = false $substr_print_fraction = 'print_fraction' $print_fraction_101016 = false $substr_array_capitalize = 'array_capitalize' $array_capitalize_101016 = false $substr_array_get_words = 'array_get_words' $array_get_words_31316 = false $substr_array_get_1st_letter = 'array_get_1st_letter' $array_array_get_1st_letter = false $substr_array_get_next_loop = 'array_get_next_loop' $array_get_next_loop = false $substr_array_get_next_break = 'array_get_next_break' $array_get_next_break = false $substr_multiply_fraction = 'do_fraction' $array_multiply_fraction = (int) 0 $substr_change_to_italic = 'change_to_italic' $array_change_to_italic = false $match = array( (int) 0 => 'print_fraction(45,150)', (int) 1 => '45,150', (int) 2 => ')' ) $count_check = array( (int) 0 => '+', (int) 1 => '0,3/10' ) $arr_caculoid = array( (int) 0 => '+', (int) 1 => '-', (int) 2 => '*', (int) 3 => '/' ) $two_fraction = array( (int) 0 => '0', (int) 1 => '3/10' ) $findme2 = '.' $search_tu = false $search_tu2 = false $search_mau = (int) 1 $search_mau2 = false $tuOne = '0' $mauOne = (int) 1 $split_mau = array( (int) 0 => '3', (int) 1 => '10' ) $tuTwo = '3' $mauTwo = '10' $k1 = (int) 29 $v1 = ''CommonComponent::generateAdvClone() - APP/Controller/Component/CommonComponent.php, line 4554 ClonesController::index2() - APP/Controller/ClonesController.php, line 2226 ReflectionMethod::invokeArgs() - [internal], line ?? Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167 [main] - APP/webroot/index.php, line 119
Notice (8): Undefined variable: mauMain [APP/Controller/Component/CommonComponent.php, line 4563]Code Context
}
if($tuMain%$mauMain === 0)
$clone = array( 'id' => '15402', 'chart' => '', 'question_id' => '44163', 'clone_type' => '1', 'phpfile' => null, 'clone_symbol' => null, 'clone_content' => '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>', 'clone_solution_step' => '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h', 'clone_answer' => '(a) 0$(t8) $(m10); (b) $(n20) km/h ', 'array' => object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} }, 'clone_image' => null, 'clone_solution_step_image' => null, 'clone_answer_image' => null, 'status' => true, 'created' => '2019-09-08 23:34:33', 'modified' => '2019-09-09 10:39:12', 'original_question' => 'Kenny and Jerry started on a 50-kim cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 40 km, Kenny cycled faster than Jerry. He arrived at the fining point 40 minutes before Jerry who was 10 km behind him. Jerry did not change his speed throughout and completed it at 11 30. <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was Kenny's average speed for the remaining 40 km of the trip in km/h?</li> </ol>', 'formula' => array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ), 'time_value' => array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ), 'criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'type_criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'image_gridline' => '', 'code_gridline' => '', 'level' => '', 'topic_id' => '', 'source' => '', 'question_code' => 'P6.SP.JC.19090801-A1', 'tag' => '', 'mark' => '', 'text_working' => '["","","","","","","","","","","","","","","\/\/","","","","","","","","","","","$(n40) \u00f7 $(h2) = $(n20)","","","",""]', 'original_solution' => '(a)<br /> Jerry's average speed<br /> = 10 ÷ <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 15 km/h<br /> <br /> Time that Jerry took for the trip<br /> = 50 ÷ 15<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h<br /> <br /> 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h before 11 30 is 08 10.<br /> <br /> (b)<br /> Time that Kenny took for the remaining 40 km of the trip<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 2 h<br /> <br /> Kenny's average speed<br /> = 40 ÷ 2<br /> = 20 km/h<br /> <br /> Answer(s): (a) 08 10; (b) 20 km/h', 'delete_by' => null, 'delete_date' => null ) $Array1 = object(Array1) { table => 'array1s' validate => array() useDbConfig => 'default' useTable => 'array1s' id => '61' data => array() schemaName => 'ischoolb_orgi' primaryKey => 'id' validationErrors => array() validationDomain => null tablePrefix => '' plugin => null name => 'Array1' alias => 'Array1' tableToModel => array( 'array1s' => 'Array1' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => array( 'id' => array( [maximum depth reached] ), 'name' => array( [maximum depth reached] ), 'content' => array( [maximum depth reached] ), 'note' => array( [maximum depth reached] ), 'created' => array( [maximum depth reached] ), 'modified' => array( [maximum depth reached] ) ) [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => true [protected] _eventManager => object(CakeEventManager) {} [protected] _validator => null } $Prime = object(AppModel) { useDbConfig => 'default' useTable => 'primes' id => false data => array() schemaName => null table => 'primes' primaryKey => 'id' validate => array() validationErrors => array() validationDomain => null plugin => null name => 'Prime' alias => 'Prime' tableToModel => array( 'primes' => 'Prime' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => null [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => false [protected] _eventManager => null [protected] _validator => null } $answer_fix = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $count_crition = (int) 51 $count_array_break = (int) 0 $count_variable_nnt = (int) 0 $message_nnt = '' $field = 'time_value' $array_get = array( (int) 0 => 'n10', (int) 8 => 'n50', (int) 9 => 'n50', (int) 6 => 'n10', (int) 2 => 't40', (int) 14 => 'h11', (int) 18 => 'm30', (int) 1 => '(n40)', (int) 25 => '(n40)', (int) 3 => '(t60)', (int) 4 => '(st60)', (int) 5 => '(st60)', (int) 22 => '(st60)', (int) 7 => '(n15)', (int) 10 => '(n15)', (int) 28 => '(n15)', (int) 20 => '(h3)', (int) 21 => '(h3)', (int) 11 => '(z)', (int) 12 => '(sz)', (int) 13 => '(sz)', (int) 15 => '(t1)', (int) 16 => '(w)', (int) 17 => '(w)', (int) 19 => '(m10)' ) $tempt = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $list_name_array = array( (int) 0 => 'Julian', (int) 1 => 'Brandon' ) $list_array_item = array( 'Jerry' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 5, 'manyArray' => '1', 'capitalize' => '0' ), 'Kenny' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 12, 'manyArray' => '1', 'capitalize' => '0' ) ) $list_italic = array() $array_variable = object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} } $question_content = '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>' $solution_step = '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h' $clone_answer = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $formula = array( (int) 0 => '45-15=30', (int) 1 => 'if(more_than(30>20))continue', (int) 2 => 'print_fraction(6,60)=6/60', (int) 3 => 'simplify_fraction(6/60)=1/10', (int) 4 => 'get_numerator(1/10)=1', (int) 5 => 'get_denominator(1/10)=10', (int) 6 => '15/1*10=150', (int) 7 => 'if(whole_number(150))continue', (int) 8 => 'get_quotient(45,150)=0', (int) 9 => 'get_remainder(45,150)=45', (int) 10 => 'print_fraction(45,150)=45/150', (int) 11 => 'simplify_fraction(45/150)=3/10', (int) 12 => 'get_numerator(3/10)=3', (int) 13 => 'get_denominator(3/10)=10', (int) 14 => '7-0=7', (int) 15 => '3/10*60=18', (int) 16 => 'if(more_than(18>9))continue', (int) 17 => 'if(whole_number(18))continue', (int) 18 => '30-18=12', (int) 19 => 'if(more_than(12>9))continue', (int) 20 => 'do_fraction(+:0,3/10)=$(hw)', (int) 21 => 'if(more_than(0>0))continue', (int) 22 => 'do_fraction(+:1/10,1/10)=$(2sz)', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2)', (int) 24 => 'if(more_than($(h2)>1))continue', (int) 25 => 'do_fraction(/:30,$(h2))=$(n20s)', (int) 26 => 'simplify_fraction($(n20s))=$(n20)', (int) 27 => 'if(more_than($(n20)>35))back', (int) 28 => 'if(more_than($(n20)>150))continue', (int) 29 => '' ) $formula_1 = array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ) $criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $type_criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $time_value = array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ) $k = '1567995994231' $v = object(stdClass) { cate => 'items' name => 'Kenny' range => '61' attr => object(stdClass) {} } $array_system = array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ) $dem_array_trung = (int) 1 $value_rand_check = (int) 12 $value_check = 'Brandon' $tempt_array = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $tempt_k = (int) 4 $tempt_v = '30' $check_who_nnt = (int) 0 $from = '7' $to = '9' $findme = '/' $arr_variable = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon', '(n40)' => (int) 30, '(t60)' => '6/60', '(st60)' => '1/10', '(tt2)' => (int) 1, '(tt3)' => (int) 10, '(n15)' => (int) 150, '(h3)' => '0', '(r3)' => '45', '(z)' => '45/150', '(sz)' => '3/10', '(t1)' => (int) 3, '(t3)' => (int) 10, '(t8)' => (int) 7, '(w)' => (float) 18, '(m10)' => (int) 12 ) $variable_k = '(m10)' $variable_v = '12' $formula_k = (int) 20 $formula_v = 'do_fraction(+:$(h3),$(sz))=$(hw)' $criterion_k = (int) 29 $criterion_v = '' $type_criterion_k = (int) 29 $type_criterion_v = '' $variable_show = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon' ) $start = 'do_fraction(' $end = ')' $array_mixed_nnt = array() $check_changes = '' $criterion_continue = '))=$(hw)' $criterion_back = '(hw)' $type_criterion_action = (int) 1 $get_between = '+:0,3/10' $type_cri = 'more_than' $get_between_value = '12>9' $bieuthuc = array( (int) 0 => 'do_fraction(+:0,3/10)', (int) 1 => '(hw)' ) $substr_pos = 'change_decimal_to_fraction' $get_numerator = false $get_whole_number_nnt = false $pos = false $giatri = '' $substr_simplify_frac = 'simplify_fraction' $simplify_frac = false $substr_simplify_ratio = 'simplify_ratio' $simplify_ratio = false $substr_get_element_of_ratio = 'get_element' $get_element_of_ratio = false $substr_numberto2decimal = 'change_number_to_2dp' $change_to_2dp = false $substr_digit_5_0 = 'change_to_2dp_with_5_or_0' $change_to_2dp_5_or_0 = false $substr_mixed_num = 'change_improper_to_mixed_number' $mixed_num = false $substr_mixed_to_improper = 'change_mixed_number_to_improper' $mixed_to_improper = false $substr_invert_fraction = 'invert_fraction' $invert_fraction = false $substr_get_same_numerator = 'share_same_numerator' $get_same_numerator = false $substr_get_same_denominator = 'share_same_denominator' $get_same_denominator = false $substr_reduce_into_ratio = 'simplify_any_into_ratio' $reduce_into_ratio = false $substr_multiply_subscript = 'multiply_ratio_subscript' $multiply_subscript = false $substr_assign = 'assign' $assign = false $substr_is_12_hour_time_am_pm = 'get_12_hour_time_am_pm' $is_12_hour_time_am_pm = false $substr_is_2400_hour_time = 'get_2400_hour_time' $is_2400_hour_time = false $substr_add_or_minus_time = 'add_or_minus_min_or_s' $add_or_minus_time = false $substr_change_percentage_to_frac = 'change_percentage_to_frac' $change_percentage_to_frac = false $substr_round_2_decimal = 'round_2_decimal_place' $round_2_decimal_place = false $substr_round_1_decimal = 'round_1_decimal_place' $round_1_decimal_place = false $substr_get_quotient = 'get_quotient' $get_quotient = false $substr_get_remainder = 'get_remainder' $get_remainder = false $substr_change_min_to_hour_min = 'change_min_to_h_min' $change_min_to_hour_min = false $substr_change_h_min_to_min = 'change_h_min_to_min' $change_h_min_to_min = false $substr_carry_1 = 'carry_1_from_mixed_number' $get_carry_1 = false $change_d_or_p_to_fraction = 'change_to_unsimplied_fraction' $get_change_d_or_p_to_fraction = false $round_off_to_nearest_ten = 'round_off_to_nearest_ten' $get_round_off_to_nearest_ten = false $round_off_to_nearest_hundred = 'round_off_to_nearest_hundred' $get_round_off_to_nearest_hundred = false $round_off_to_nearest_thousand = 'round_off_to_nearest_thousand' $get_round_off_to_nearest_thousand = false $change_12_to_24 = 'change_12h_to_24h' $get_12_to_24 = false $change_24_to_12 = 'change_24h_to_12h' $get_24_to_12 = false $get_factors = 'get_factors' $get_factors_nnt = false $get_common_factors = 'get_common_factors' $get_common_factors_nnt = false $get_multiples = 'get_multiples' $get_multiples_23916 = false $get_add_or_minus_multiples = 'add_or_minus_multiples' $add_or_minus_multiples_23916 = false $get_common_numbers = 'get_common_numbers' $get_common_numbers_240916 = false $substr_array_singular = 'array_singular' $array_singular_101016 = false $substr_array_plural = 'array_plural' $array_plural_101016 = false $substr_print_fraction = 'print_fraction' $print_fraction_101016 = false $substr_array_capitalize = 'array_capitalize' $array_capitalize_101016 = false $substr_array_get_words = 'array_get_words' $array_get_words_31316 = false $substr_array_get_1st_letter = 'array_get_1st_letter' $array_array_get_1st_letter = false $substr_array_get_next_loop = 'array_get_next_loop' $array_get_next_loop = false $substr_array_get_next_break = 'array_get_next_break' $array_get_next_break = false $substr_multiply_fraction = 'do_fraction' $array_multiply_fraction = (int) 0 $substr_change_to_italic = 'change_to_italic' $array_change_to_italic = false $match = array( (int) 0 => 'print_fraction(45,150)', (int) 1 => '45,150', (int) 2 => ')' ) $count_check = array( (int) 0 => '+', (int) 1 => '0,3/10' ) $arr_caculoid = array( (int) 0 => '+', (int) 1 => '-', (int) 2 => '*', (int) 3 => '/' ) $two_fraction = array( (int) 0 => '0', (int) 1 => '3/10' ) $findme2 = '.' $search_tu = false $search_tu2 = false $search_mau = (int) 1 $search_mau2 = false $tuOne = '0' $mauOne = (int) 1 $split_mau = array( (int) 0 => '3', (int) 1 => '10' ) $tuTwo = '3' $mauTwo = '10' $k1 = (int) 29 $v1 = ''CommonComponent::generateAdvClone() - APP/Controller/Component/CommonComponent.php, line 4563 ClonesController::index2() - APP/Controller/ClonesController.php, line 2226 ReflectionMethod::invokeArgs() - [internal], line ?? Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167 [main] - APP/webroot/index.php, line 119
Notice (8): Undefined variable: tuMain [APP/Controller/Component/CommonComponent.php, line 4563]Code Context
}
if($tuMain%$mauMain === 0)
$clone = array( 'id' => '15402', 'chart' => '', 'question_id' => '44163', 'clone_type' => '1', 'phpfile' => null, 'clone_symbol' => null, 'clone_content' => '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>', 'clone_solution_step' => '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h', 'clone_answer' => '(a) 0$(t8) $(m10); (b) $(n20) km/h ', 'array' => object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} }, 'clone_image' => null, 'clone_solution_step_image' => null, 'clone_answer_image' => null, 'status' => true, 'created' => '2019-09-08 23:34:33', 'modified' => '2019-09-09 10:39:12', 'original_question' => 'Kenny and Jerry started on a 50-kim cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 40 km, Kenny cycled faster than Jerry. He arrived at the fining point 40 minutes before Jerry who was 10 km behind him. Jerry did not change his speed throughout and completed it at 11 30. <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was Kenny's average speed for the remaining 40 km of the trip in km/h?</li> </ol>', 'formula' => array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ), 'time_value' => array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ), 'criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'type_criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'image_gridline' => '', 'code_gridline' => '', 'level' => '', 'topic_id' => '', 'source' => '', 'question_code' => 'P6.SP.JC.19090801-A1', 'tag' => '', 'mark' => '', 'text_working' => '["","","","","","","","","","","","","","","\/\/","","","","","","","","","","","$(n40) \u00f7 $(h2) = $(n20)","","","",""]', 'original_solution' => '(a)<br /> Jerry's average speed<br /> = 10 ÷ <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 15 km/h<br /> <br /> Time that Jerry took for the trip<br /> = 50 ÷ 15<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h<br /> <br /> 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h before 11 30 is 08 10.<br /> <br /> (b)<br /> Time that Kenny took for the remaining 40 km of the trip<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 2 h<br /> <br /> Kenny's average speed<br /> = 40 ÷ 2<br /> = 20 km/h<br /> <br /> Answer(s): (a) 08 10; (b) 20 km/h', 'delete_by' => null, 'delete_date' => null ) $Array1 = object(Array1) { table => 'array1s' validate => array() useDbConfig => 'default' useTable => 'array1s' id => '61' data => array() schemaName => 'ischoolb_orgi' primaryKey => 'id' validationErrors => array() validationDomain => null tablePrefix => '' plugin => null name => 'Array1' alias => 'Array1' tableToModel => array( 'array1s' => 'Array1' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => array( 'id' => array( [maximum depth reached] ), 'name' => array( [maximum depth reached] ), 'content' => array( [maximum depth reached] ), 'note' => array( [maximum depth reached] ), 'created' => array( [maximum depth reached] ), 'modified' => array( [maximum depth reached] ) ) [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => true [protected] _eventManager => object(CakeEventManager) {} [protected] _validator => null } $Prime = object(AppModel) { useDbConfig => 'default' useTable => 'primes' id => false data => array() schemaName => null table => 'primes' primaryKey => 'id' validate => array() validationErrors => array() validationDomain => null plugin => null name => 'Prime' alias => 'Prime' tableToModel => array( 'primes' => 'Prime' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => null [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => false [protected] _eventManager => null [protected] _validator => null } $answer_fix = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $count_crition = (int) 51 $count_array_break = (int) 0 $count_variable_nnt = (int) 0 $message_nnt = '' $field = 'time_value' $array_get = array( (int) 0 => 'n10', (int) 8 => 'n50', (int) 9 => 'n50', (int) 6 => 'n10', (int) 2 => 't40', (int) 14 => 'h11', (int) 18 => 'm30', (int) 1 => '(n40)', (int) 25 => '(n40)', (int) 3 => '(t60)', (int) 4 => '(st60)', (int) 5 => '(st60)', (int) 22 => '(st60)', (int) 7 => '(n15)', (int) 10 => '(n15)', (int) 28 => '(n15)', (int) 20 => '(h3)', (int) 21 => '(h3)', (int) 11 => '(z)', (int) 12 => '(sz)', (int) 13 => '(sz)', (int) 15 => '(t1)', (int) 16 => '(w)', (int) 17 => '(w)', (int) 19 => '(m10)' ) $tempt = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $list_name_array = array( (int) 0 => 'Julian', (int) 1 => 'Brandon' ) $list_array_item = array( 'Jerry' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 5, 'manyArray' => '1', 'capitalize' => '0' ), 'Kenny' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 12, 'manyArray' => '1', 'capitalize' => '0' ) ) $list_italic = array() $array_variable = object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} } $question_content = '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>' $solution_step = '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h' $clone_answer = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $formula = array( (int) 0 => '45-15=30', (int) 1 => 'if(more_than(30>20))continue', (int) 2 => 'print_fraction(6,60)=6/60', (int) 3 => 'simplify_fraction(6/60)=1/10', (int) 4 => 'get_numerator(1/10)=1', (int) 5 => 'get_denominator(1/10)=10', (int) 6 => '15/1*10=150', (int) 7 => 'if(whole_number(150))continue', (int) 8 => 'get_quotient(45,150)=0', (int) 9 => 'get_remainder(45,150)=45', (int) 10 => 'print_fraction(45,150)=45/150', (int) 11 => 'simplify_fraction(45/150)=3/10', (int) 12 => 'get_numerator(3/10)=3', (int) 13 => 'get_denominator(3/10)=10', (int) 14 => '7-0=7', (int) 15 => '3/10*60=18', (int) 16 => 'if(more_than(18>9))continue', (int) 17 => 'if(whole_number(18))continue', (int) 18 => '30-18=12', (int) 19 => 'if(more_than(12>9))continue', (int) 20 => 'do_fraction(+:0,3/10)=$(hw)', (int) 21 => 'if(more_than(0>0))continue', (int) 22 => 'do_fraction(+:1/10,1/10)=$(2sz)', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2)', (int) 24 => 'if(more_than($(h2)>1))continue', (int) 25 => 'do_fraction(/:30,$(h2))=$(n20s)', (int) 26 => 'simplify_fraction($(n20s))=$(n20)', (int) 27 => 'if(more_than($(n20)>35))back', (int) 28 => 'if(more_than($(n20)>150))continue', (int) 29 => '' ) $formula_1 = array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ) $criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $type_criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $time_value = array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ) $k = '1567995994231' $v = object(stdClass) { cate => 'items' name => 'Kenny' range => '61' attr => object(stdClass) {} } $array_system = array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ) $dem_array_trung = (int) 1 $value_rand_check = (int) 12 $value_check = 'Brandon' $tempt_array = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $tempt_k = (int) 4 $tempt_v = '30' $check_who_nnt = (int) 0 $from = '7' $to = '9' $findme = '/' $arr_variable = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon', '(n40)' => (int) 30, '(t60)' => '6/60', '(st60)' => '1/10', '(tt2)' => (int) 1, '(tt3)' => (int) 10, '(n15)' => (int) 150, '(h3)' => '0', '(r3)' => '45', '(z)' => '45/150', '(sz)' => '3/10', '(t1)' => (int) 3, '(t3)' => (int) 10, '(t8)' => (int) 7, '(w)' => (float) 18, '(m10)' => (int) 12 ) $variable_k = '(m10)' $variable_v = '12' $formula_k = (int) 20 $formula_v = 'do_fraction(+:$(h3),$(sz))=$(hw)' $criterion_k = (int) 29 $criterion_v = '' $type_criterion_k = (int) 29 $type_criterion_v = '' $variable_show = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon' ) $start = 'do_fraction(' $end = ')' $array_mixed_nnt = array() $check_changes = '' $criterion_continue = '))=$(hw)' $criterion_back = '(hw)' $type_criterion_action = (int) 1 $get_between = '+:0,3/10' $type_cri = 'more_than' $get_between_value = '12>9' $bieuthuc = array( (int) 0 => 'do_fraction(+:0,3/10)', (int) 1 => '(hw)' ) $substr_pos = 'change_decimal_to_fraction' $get_numerator = false $get_whole_number_nnt = false $pos = false $giatri = '' $substr_simplify_frac = 'simplify_fraction' $simplify_frac = false $substr_simplify_ratio = 'simplify_ratio' $simplify_ratio = false $substr_get_element_of_ratio = 'get_element' $get_element_of_ratio = false $substr_numberto2decimal = 'change_number_to_2dp' $change_to_2dp = false $substr_digit_5_0 = 'change_to_2dp_with_5_or_0' $change_to_2dp_5_or_0 = false $substr_mixed_num = 'change_improper_to_mixed_number' $mixed_num = false $substr_mixed_to_improper = 'change_mixed_number_to_improper' $mixed_to_improper = false $substr_invert_fraction = 'invert_fraction' $invert_fraction = false $substr_get_same_numerator = 'share_same_numerator' $get_same_numerator = false $substr_get_same_denominator = 'share_same_denominator' $get_same_denominator = false $substr_reduce_into_ratio = 'simplify_any_into_ratio' $reduce_into_ratio = false $substr_multiply_subscript = 'multiply_ratio_subscript' $multiply_subscript = false $substr_assign = 'assign' $assign = false $substr_is_12_hour_time_am_pm = 'get_12_hour_time_am_pm' $is_12_hour_time_am_pm = false $substr_is_2400_hour_time = 'get_2400_hour_time' $is_2400_hour_time = false $substr_add_or_minus_time = 'add_or_minus_min_or_s' $add_or_minus_time = false $substr_change_percentage_to_frac = 'change_percentage_to_frac' $change_percentage_to_frac = false $substr_round_2_decimal = 'round_2_decimal_place' $round_2_decimal_place = false $substr_round_1_decimal = 'round_1_decimal_place' $round_1_decimal_place = false $substr_get_quotient = 'get_quotient' $get_quotient = false $substr_get_remainder = 'get_remainder' $get_remainder = false $substr_change_min_to_hour_min = 'change_min_to_h_min' $change_min_to_hour_min = false $substr_change_h_min_to_min = 'change_h_min_to_min' $change_h_min_to_min = false $substr_carry_1 = 'carry_1_from_mixed_number' $get_carry_1 = false $change_d_or_p_to_fraction = 'change_to_unsimplied_fraction' $get_change_d_or_p_to_fraction = false $round_off_to_nearest_ten = 'round_off_to_nearest_ten' $get_round_off_to_nearest_ten = false $round_off_to_nearest_hundred = 'round_off_to_nearest_hundred' $get_round_off_to_nearest_hundred = false $round_off_to_nearest_thousand = 'round_off_to_nearest_thousand' $get_round_off_to_nearest_thousand = false $change_12_to_24 = 'change_12h_to_24h' $get_12_to_24 = false $change_24_to_12 = 'change_24h_to_12h' $get_24_to_12 = false $get_factors = 'get_factors' $get_factors_nnt = false $get_common_factors = 'get_common_factors' $get_common_factors_nnt = false $get_multiples = 'get_multiples' $get_multiples_23916 = false $get_add_or_minus_multiples = 'add_or_minus_multiples' $add_or_minus_multiples_23916 = false $get_common_numbers = 'get_common_numbers' $get_common_numbers_240916 = false $substr_array_singular = 'array_singular' $array_singular_101016 = false $substr_array_plural = 'array_plural' $array_plural_101016 = false $substr_print_fraction = 'print_fraction' $print_fraction_101016 = false $substr_array_capitalize = 'array_capitalize' $array_capitalize_101016 = false $substr_array_get_words = 'array_get_words' $array_get_words_31316 = false $substr_array_get_1st_letter = 'array_get_1st_letter' $array_array_get_1st_letter = false $substr_array_get_next_loop = 'array_get_next_loop' $array_get_next_loop = false $substr_array_get_next_break = 'array_get_next_break' $array_get_next_break = false $substr_multiply_fraction = 'do_fraction' $array_multiply_fraction = (int) 0 $substr_change_to_italic = 'change_to_italic' $array_change_to_italic = false $match = array( (int) 0 => 'print_fraction(45,150)', (int) 1 => '45,150', (int) 2 => ')' ) $count_check = array( (int) 0 => '+', (int) 1 => '0,3/10' ) $arr_caculoid = array( (int) 0 => '+', (int) 1 => '-', (int) 2 => '*', (int) 3 => '/' ) $two_fraction = array( (int) 0 => '0', (int) 1 => '3/10' ) $findme2 = '.' $search_tu = false $search_tu2 = false $search_mau = (int) 1 $search_mau2 = false $tuOne = '0' $mauOne = (int) 1 $split_mau = array( (int) 0 => '3', (int) 1 => '10' ) $tuTwo = '3' $mauTwo = '10' $k1 = (int) 29 $v1 = ''CommonComponent::generateAdvClone() - APP/Controller/Component/CommonComponent.php, line 4563 ClonesController::index2() - APP/Controller/ClonesController.php, line 2226 ReflectionMethod::invokeArgs() - [internal], line ?? Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167 [main] - APP/webroot/index.php, line 119
Warning (2): Division by zero [APP/Controller/Component/CommonComponent.php, line 4563]Code Context
}
if($tuMain%$mauMain === 0)
$clone = array( 'id' => '15402', 'chart' => '', 'question_id' => '44163', 'clone_type' => '1', 'phpfile' => null, 'clone_symbol' => null, 'clone_content' => '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>', 'clone_solution_step' => '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h', 'clone_answer' => '(a) 0$(t8) $(m10); (b) $(n20) km/h ', 'array' => object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} }, 'clone_image' => null, 'clone_solution_step_image' => null, 'clone_answer_image' => null, 'status' => true, 'created' => '2019-09-08 23:34:33', 'modified' => '2019-09-09 10:39:12', 'original_question' => 'Kenny and Jerry started on a 50-kim cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 40 km, Kenny cycled faster than Jerry. He arrived at the fining point 40 minutes before Jerry who was 10 km behind him. Jerry did not change his speed throughout and completed it at 11 30. <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was Kenny's average speed for the remaining 40 km of the trip in km/h?</li> </ol>', 'formula' => array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ), 'time_value' => array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ), 'criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'type_criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'image_gridline' => '', 'code_gridline' => '', 'level' => '', 'topic_id' => '', 'source' => '', 'question_code' => 'P6.SP.JC.19090801-A1', 'tag' => '', 'mark' => '', 'text_working' => '["","","","","","","","","","","","","","","\/\/","","","","","","","","","","","$(n40) \u00f7 $(h2) = $(n20)","","","",""]', 'original_solution' => '(a)<br /> Jerry's average speed<br /> = 10 ÷ <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 15 km/h<br /> <br /> Time that Jerry took for the trip<br /> = 50 ÷ 15<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h<br /> <br /> 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h before 11 30 is 08 10.<br /> <br /> (b)<br /> Time that Kenny took for the remaining 40 km of the trip<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 2 h<br /> <br /> Kenny's average speed<br /> = 40 ÷ 2<br /> = 20 km/h<br /> <br /> Answer(s): (a) 08 10; (b) 20 km/h', 'delete_by' => null, 'delete_date' => null ) $Array1 = object(Array1) { table => 'array1s' validate => array() useDbConfig => 'default' useTable => 'array1s' id => '61' data => array() schemaName => 'ischoolb_orgi' primaryKey => 'id' validationErrors => array() validationDomain => null tablePrefix => '' plugin => null name => 'Array1' alias => 'Array1' tableToModel => array( 'array1s' => 'Array1' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => array( 'id' => array( [maximum depth reached] ), 'name' => array( [maximum depth reached] ), 'content' => array( [maximum depth reached] ), 'note' => array( [maximum depth reached] ), 'created' => array( [maximum depth reached] ), 'modified' => array( [maximum depth reached] ) ) [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => true [protected] _eventManager => object(CakeEventManager) {} [protected] _validator => null } $Prime = object(AppModel) { useDbConfig => 'default' useTable => 'primes' id => false data => array() schemaName => null table => 'primes' primaryKey => 'id' validate => array() validationErrors => array() validationDomain => null plugin => null name => 'Prime' alias => 'Prime' tableToModel => array( 'primes' => 'Prime' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => null [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => false [protected] _eventManager => null [protected] _validator => null } $answer_fix = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $count_crition = (int) 51 $count_array_break = (int) 0 $count_variable_nnt = (int) 0 $message_nnt = '' $field = 'time_value' $array_get = array( (int) 0 => 'n10', (int) 8 => 'n50', (int) 9 => 'n50', (int) 6 => 'n10', (int) 2 => 't40', (int) 14 => 'h11', (int) 18 => 'm30', (int) 1 => '(n40)', (int) 25 => '(n40)', (int) 3 => '(t60)', (int) 4 => '(st60)', (int) 5 => '(st60)', (int) 22 => '(st60)', (int) 7 => '(n15)', (int) 10 => '(n15)', (int) 28 => '(n15)', (int) 20 => '(h3)', (int) 21 => '(h3)', (int) 11 => '(z)', (int) 12 => '(sz)', (int) 13 => '(sz)', (int) 15 => '(t1)', (int) 16 => '(w)', (int) 17 => '(w)', (int) 19 => '(m10)' ) $tempt = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $list_name_array = array( (int) 0 => 'Julian', (int) 1 => 'Brandon' ) $list_array_item = array( 'Jerry' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 5, 'manyArray' => '1', 'capitalize' => '0' ), 'Kenny' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 12, 'manyArray' => '1', 'capitalize' => '0' ) ) $list_italic = array() $array_variable = object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} } $question_content = '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>' $solution_step = '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h' $clone_answer = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $formula = array( (int) 0 => '45-15=30', (int) 1 => 'if(more_than(30>20))continue', (int) 2 => 'print_fraction(6,60)=6/60', (int) 3 => 'simplify_fraction(6/60)=1/10', (int) 4 => 'get_numerator(1/10)=1', (int) 5 => 'get_denominator(1/10)=10', (int) 6 => '15/1*10=150', (int) 7 => 'if(whole_number(150))continue', (int) 8 => 'get_quotient(45,150)=0', (int) 9 => 'get_remainder(45,150)=45', (int) 10 => 'print_fraction(45,150)=45/150', (int) 11 => 'simplify_fraction(45/150)=3/10', (int) 12 => 'get_numerator(3/10)=3', (int) 13 => 'get_denominator(3/10)=10', (int) 14 => '7-0=7', (int) 15 => '3/10*60=18', (int) 16 => 'if(more_than(18>9))continue', (int) 17 => 'if(whole_number(18))continue', (int) 18 => '30-18=12', (int) 19 => 'if(more_than(12>9))continue', (int) 20 => 'do_fraction(+:0,3/10)=$(hw)', (int) 21 => 'if(more_than(0>0))continue', (int) 22 => 'do_fraction(+:1/10,1/10)=$(2sz)', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2)', (int) 24 => 'if(more_than($(h2)>1))continue', (int) 25 => 'do_fraction(/:30,$(h2))=$(n20s)', (int) 26 => 'simplify_fraction($(n20s))=$(n20)', (int) 27 => 'if(more_than($(n20)>35))back', (int) 28 => 'if(more_than($(n20)>150))continue', (int) 29 => '' ) $formula_1 = array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ) $criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $type_criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $time_value = array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ) $k = '1567995994231' $v = object(stdClass) { cate => 'items' name => 'Kenny' range => '61' attr => object(stdClass) {} } $array_system = array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ) $dem_array_trung = (int) 1 $value_rand_check = (int) 12 $value_check = 'Brandon' $tempt_array = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $tempt_k = (int) 4 $tempt_v = '30' $check_who_nnt = (int) 0 $from = '7' $to = '9' $findme = '/' $arr_variable = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon', '(n40)' => (int) 30, '(t60)' => '6/60', '(st60)' => '1/10', '(tt2)' => (int) 1, '(tt3)' => (int) 10, '(n15)' => (int) 150, '(h3)' => '0', '(r3)' => '45', '(z)' => '45/150', '(sz)' => '3/10', '(t1)' => (int) 3, '(t3)' => (int) 10, '(t8)' => (int) 7, '(w)' => (float) 18, '(m10)' => (int) 12 ) $variable_k = '(m10)' $variable_v = '12' $formula_k = (int) 20 $formula_v = 'do_fraction(+:$(h3),$(sz))=$(hw)' $criterion_k = (int) 29 $criterion_v = '' $type_criterion_k = (int) 29 $type_criterion_v = '' $variable_show = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon' ) $start = 'do_fraction(' $end = ')' $array_mixed_nnt = array() $check_changes = '' $criterion_continue = '))=$(hw)' $criterion_back = '(hw)' $type_criterion_action = (int) 1 $get_between = '+:0,3/10' $type_cri = 'more_than' $get_between_value = '12>9' $bieuthuc = array( (int) 0 => 'do_fraction(+:0,3/10)', (int) 1 => '(hw)' ) $substr_pos = 'change_decimal_to_fraction' $get_numerator = false $get_whole_number_nnt = false $pos = false $giatri = '' $substr_simplify_frac = 'simplify_fraction' $simplify_frac = false $substr_simplify_ratio = 'simplify_ratio' $simplify_ratio = false $substr_get_element_of_ratio = 'get_element' $get_element_of_ratio = false $substr_numberto2decimal = 'change_number_to_2dp' $change_to_2dp = false $substr_digit_5_0 = 'change_to_2dp_with_5_or_0' $change_to_2dp_5_or_0 = false $substr_mixed_num = 'change_improper_to_mixed_number' $mixed_num = false $substr_mixed_to_improper = 'change_mixed_number_to_improper' $mixed_to_improper = false $substr_invert_fraction = 'invert_fraction' $invert_fraction = false $substr_get_same_numerator = 'share_same_numerator' $get_same_numerator = false $substr_get_same_denominator = 'share_same_denominator' $get_same_denominator = false $substr_reduce_into_ratio = 'simplify_any_into_ratio' $reduce_into_ratio = false $substr_multiply_subscript = 'multiply_ratio_subscript' $multiply_subscript = false $substr_assign = 'assign' $assign = false $substr_is_12_hour_time_am_pm = 'get_12_hour_time_am_pm' $is_12_hour_time_am_pm = false $substr_is_2400_hour_time = 'get_2400_hour_time' $is_2400_hour_time = false $substr_add_or_minus_time = 'add_or_minus_min_or_s' $add_or_minus_time = false $substr_change_percentage_to_frac = 'change_percentage_to_frac' $change_percentage_to_frac = false $substr_round_2_decimal = 'round_2_decimal_place' $round_2_decimal_place = false $substr_round_1_decimal = 'round_1_decimal_place' $round_1_decimal_place = false $substr_get_quotient = 'get_quotient' $get_quotient = false $substr_get_remainder = 'get_remainder' $get_remainder = false $substr_change_min_to_hour_min = 'change_min_to_h_min' $change_min_to_hour_min = false $substr_change_h_min_to_min = 'change_h_min_to_min' $change_h_min_to_min = false $substr_carry_1 = 'carry_1_from_mixed_number' $get_carry_1 = false $change_d_or_p_to_fraction = 'change_to_unsimplied_fraction' $get_change_d_or_p_to_fraction = false $round_off_to_nearest_ten = 'round_off_to_nearest_ten' $get_round_off_to_nearest_ten = false $round_off_to_nearest_hundred = 'round_off_to_nearest_hundred' $get_round_off_to_nearest_hundred = false $round_off_to_nearest_thousand = 'round_off_to_nearest_thousand' $get_round_off_to_nearest_thousand = false $change_12_to_24 = 'change_12h_to_24h' $get_12_to_24 = false $change_24_to_12 = 'change_24h_to_12h' $get_24_to_12 = false $get_factors = 'get_factors' $get_factors_nnt = false $get_common_factors = 'get_common_factors' $get_common_factors_nnt = false $get_multiples = 'get_multiples' $get_multiples_23916 = false $get_add_or_minus_multiples = 'add_or_minus_multiples' $add_or_minus_multiples_23916 = false $get_common_numbers = 'get_common_numbers' $get_common_numbers_240916 = false $substr_array_singular = 'array_singular' $array_singular_101016 = false $substr_array_plural = 'array_plural' $array_plural_101016 = false $substr_print_fraction = 'print_fraction' $print_fraction_101016 = false $substr_array_capitalize = 'array_capitalize' $array_capitalize_101016 = false $substr_array_get_words = 'array_get_words' $array_get_words_31316 = false $substr_array_get_1st_letter = 'array_get_1st_letter' $array_array_get_1st_letter = false $substr_array_get_next_loop = 'array_get_next_loop' $array_get_next_loop = false $substr_array_get_next_break = 'array_get_next_break' $array_get_next_break = false $substr_multiply_fraction = 'do_fraction' $array_multiply_fraction = (int) 0 $substr_change_to_italic = 'change_to_italic' $array_change_to_italic = false $match = array( (int) 0 => 'print_fraction(45,150)', (int) 1 => '45,150', (int) 2 => ')' ) $count_check = array( (int) 0 => '+', (int) 1 => '0,3/10' ) $arr_caculoid = array( (int) 0 => '+', (int) 1 => '-', (int) 2 => '*', (int) 3 => '/' ) $two_fraction = array( (int) 0 => '0', (int) 1 => '3/10' ) $findme2 = '.' $search_tu = false $search_tu2 = false $search_mau = (int) 1 $search_mau2 = false $tuOne = '0' $mauOne = (int) 1 $split_mau = array( (int) 0 => '3', (int) 1 => '10' ) $tuTwo = '3' $mauTwo = '10' $k1 = (int) 29 $v1 = ''CommonComponent::generateAdvClone() - APP/Controller/Component/CommonComponent.php, line 4563 ClonesController::index2() - APP/Controller/ClonesController.php, line 2226 ReflectionMethod::invokeArgs() - [internal], line ?? Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167 [main] - APP/webroot/index.php, line 119
Notice (8): Undefined variable: tuMain [APP/Controller/Component/CommonComponent.php, line 4567]Code Context$giatri = $tuMain/$mauMain;
}else{
$giatri = $tuMain.'/'.$mauMain;
$clone = array( 'id' => '15402', 'chart' => '', 'question_id' => '44163', 'clone_type' => '1', 'phpfile' => null, 'clone_symbol' => null, 'clone_content' => '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>', 'clone_solution_step' => '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h', 'clone_answer' => '(a) 0$(t8) $(m10); (b) $(n20) km/h ', 'array' => object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} }, 'clone_image' => null, 'clone_solution_step_image' => null, 'clone_answer_image' => null, 'status' => true, 'created' => '2019-09-08 23:34:33', 'modified' => '2019-09-09 10:39:12', 'original_question' => 'Kenny and Jerry started on a 50-kim cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 40 km, Kenny cycled faster than Jerry. He arrived at the fining point 40 minutes before Jerry who was 10 km behind him. Jerry did not change his speed throughout and completed it at 11 30. <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was Kenny's average speed for the remaining 40 km of the trip in km/h?</li> </ol>', 'formula' => array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ), 'time_value' => array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ), 'criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'type_criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'image_gridline' => '', 'code_gridline' => '', 'level' => '', 'topic_id' => '', 'source' => '', 'question_code' => 'P6.SP.JC.19090801-A1', 'tag' => '', 'mark' => '', 'text_working' => '["","","","","","","","","","","","","","","\/\/","","","","","","","","","","","$(n40) \u00f7 $(h2) = $(n20)","","","",""]', 'original_solution' => '(a)<br /> Jerry's average speed<br /> = 10 ÷ <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 15 km/h<br /> <br /> Time that Jerry took for the trip<br /> = 50 ÷ 15<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h<br /> <br /> 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h before 11 30 is 08 10.<br /> <br /> (b)<br /> Time that Kenny took for the remaining 40 km of the trip<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 2 h<br /> <br /> Kenny's average speed<br /> = 40 ÷ 2<br /> = 20 km/h<br /> <br /> Answer(s): (a) 08 10; (b) 20 km/h', 'delete_by' => null, 'delete_date' => null ) $Array1 = object(Array1) { table => 'array1s' validate => array() useDbConfig => 'default' useTable => 'array1s' id => '61' data => array() schemaName => 'ischoolb_orgi' primaryKey => 'id' validationErrors => array() validationDomain => null tablePrefix => '' plugin => null name => 'Array1' alias => 'Array1' tableToModel => array( 'array1s' => 'Array1' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => array( 'id' => array( [maximum depth reached] ), 'name' => array( [maximum depth reached] ), 'content' => array( [maximum depth reached] ), 'note' => array( [maximum depth reached] ), 'created' => array( [maximum depth reached] ), 'modified' => array( [maximum depth reached] ) ) [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => true [protected] _eventManager => object(CakeEventManager) {} [protected] _validator => null } $Prime = object(AppModel) { useDbConfig => 'default' useTable => 'primes' id => false data => array() schemaName => null table => 'primes' primaryKey => 'id' validate => array() validationErrors => array() validationDomain => null plugin => null name => 'Prime' alias => 'Prime' tableToModel => array( 'primes' => 'Prime' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => null [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => false [protected] _eventManager => null [protected] _validator => null } $answer_fix = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $count_crition = (int) 51 $count_array_break = (int) 0 $count_variable_nnt = (int) 0 $message_nnt = '' $field = 'time_value' $array_get = array( (int) 0 => 'n10', (int) 8 => 'n50', (int) 9 => 'n50', (int) 6 => 'n10', (int) 2 => 't40', (int) 14 => 'h11', (int) 18 => 'm30', (int) 1 => '(n40)', (int) 25 => '(n40)', (int) 3 => '(t60)', (int) 4 => '(st60)', (int) 5 => '(st60)', (int) 22 => '(st60)', (int) 7 => '(n15)', (int) 10 => '(n15)', (int) 28 => '(n15)', (int) 20 => '(h3)', (int) 21 => '(h3)', (int) 11 => '(z)', (int) 12 => '(sz)', (int) 13 => '(sz)', (int) 15 => '(t1)', (int) 16 => '(w)', (int) 17 => '(w)', (int) 19 => '(m10)' ) $tempt = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $list_name_array = array( (int) 0 => 'Julian', (int) 1 => 'Brandon' ) $list_array_item = array( 'Jerry' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 5, 'manyArray' => '1', 'capitalize' => '0' ), 'Kenny' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 12, 'manyArray' => '1', 'capitalize' => '0' ) ) $list_italic = array() $array_variable = object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} } $question_content = '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>' $solution_step = '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h' $clone_answer = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $formula = array( (int) 0 => '45-15=30', (int) 1 => 'if(more_than(30>20))continue', (int) 2 => 'print_fraction(6,60)=6/60', (int) 3 => 'simplify_fraction(6/60)=1/10', (int) 4 => 'get_numerator(1/10)=1', (int) 5 => 'get_denominator(1/10)=10', (int) 6 => '15/1*10=150', (int) 7 => 'if(whole_number(150))continue', (int) 8 => 'get_quotient(45,150)=0', (int) 9 => 'get_remainder(45,150)=45', (int) 10 => 'print_fraction(45,150)=45/150', (int) 11 => 'simplify_fraction(45/150)=3/10', (int) 12 => 'get_numerator(3/10)=3', (int) 13 => 'get_denominator(3/10)=10', (int) 14 => '7-0=7', (int) 15 => '3/10*60=18', (int) 16 => 'if(more_than(18>9))continue', (int) 17 => 'if(whole_number(18))continue', (int) 18 => '30-18=12', (int) 19 => 'if(more_than(12>9))continue', (int) 20 => 'do_fraction(+:0,3/10)=$(hw)', (int) 21 => 'if(more_than(0>0))continue', (int) 22 => 'do_fraction(+:1/10,1/10)=$(2sz)', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2)', (int) 24 => 'if(more_than($(h2)>1))continue', (int) 25 => 'do_fraction(/:30,$(h2))=$(n20s)', (int) 26 => 'simplify_fraction($(n20s))=$(n20)', (int) 27 => 'if(more_than($(n20)>35))back', (int) 28 => 'if(more_than($(n20)>150))continue', (int) 29 => '' ) $formula_1 = array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ) $criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $type_criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $time_value = array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ) $k = '1567995994231' $v = object(stdClass) { cate => 'items' name => 'Kenny' range => '61' attr => object(stdClass) {} } $array_system = array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ) $dem_array_trung = (int) 1 $value_rand_check = (int) 12 $value_check = 'Brandon' $tempt_array = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $tempt_k = (int) 4 $tempt_v = '30' $check_who_nnt = (int) 0 $from = '7' $to = '9' $findme = '/' $arr_variable = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon', '(n40)' => (int) 30, '(t60)' => '6/60', '(st60)' => '1/10', '(tt2)' => (int) 1, '(tt3)' => (int) 10, '(n15)' => (int) 150, '(h3)' => '0', '(r3)' => '45', '(z)' => '45/150', '(sz)' => '3/10', '(t1)' => (int) 3, '(t3)' => (int) 10, '(t8)' => (int) 7, '(w)' => (float) 18, '(m10)' => (int) 12 ) $variable_k = '(m10)' $variable_v = '12' $formula_k = (int) 20 $formula_v = 'do_fraction(+:$(h3),$(sz))=$(hw)' $criterion_k = (int) 29 $criterion_v = '' $type_criterion_k = (int) 29 $type_criterion_v = '' $variable_show = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon' ) $start = 'do_fraction(' $end = ')' $array_mixed_nnt = array() $check_changes = '' $criterion_continue = '))=$(hw)' $criterion_back = '(hw)' $type_criterion_action = (int) 1 $get_between = '+:0,3/10' $type_cri = 'more_than' $get_between_value = '12>9' $bieuthuc = array( (int) 0 => 'do_fraction(+:0,3/10)', (int) 1 => '(hw)' ) $substr_pos = 'change_decimal_to_fraction' $get_numerator = false $get_whole_number_nnt = false $pos = false $giatri = '' $substr_simplify_frac = 'simplify_fraction' $simplify_frac = false $substr_simplify_ratio = 'simplify_ratio' $simplify_ratio = false $substr_get_element_of_ratio = 'get_element' $get_element_of_ratio = false $substr_numberto2decimal = 'change_number_to_2dp' $change_to_2dp = false $substr_digit_5_0 = 'change_to_2dp_with_5_or_0' $change_to_2dp_5_or_0 = false $substr_mixed_num = 'change_improper_to_mixed_number' $mixed_num = false $substr_mixed_to_improper = 'change_mixed_number_to_improper' $mixed_to_improper = false $substr_invert_fraction = 'invert_fraction' $invert_fraction = false $substr_get_same_numerator = 'share_same_numerator' $get_same_numerator = false $substr_get_same_denominator = 'share_same_denominator' $get_same_denominator = false $substr_reduce_into_ratio = 'simplify_any_into_ratio' $reduce_into_ratio = false $substr_multiply_subscript = 'multiply_ratio_subscript' $multiply_subscript = false $substr_assign = 'assign' $assign = false $substr_is_12_hour_time_am_pm = 'get_12_hour_time_am_pm' $is_12_hour_time_am_pm = false $substr_is_2400_hour_time = 'get_2400_hour_time' $is_2400_hour_time = false $substr_add_or_minus_time = 'add_or_minus_min_or_s' $add_or_minus_time = false $substr_change_percentage_to_frac = 'change_percentage_to_frac' $change_percentage_to_frac = false $substr_round_2_decimal = 'round_2_decimal_place' $round_2_decimal_place = false $substr_round_1_decimal = 'round_1_decimal_place' $round_1_decimal_place = false $substr_get_quotient = 'get_quotient' $get_quotient = false $substr_get_remainder = 'get_remainder' $get_remainder = false $substr_change_min_to_hour_min = 'change_min_to_h_min' $change_min_to_hour_min = false $substr_change_h_min_to_min = 'change_h_min_to_min' $change_h_min_to_min = false $substr_carry_1 = 'carry_1_from_mixed_number' $get_carry_1 = false $change_d_or_p_to_fraction = 'change_to_unsimplied_fraction' $get_change_d_or_p_to_fraction = false $round_off_to_nearest_ten = 'round_off_to_nearest_ten' $get_round_off_to_nearest_ten = false $round_off_to_nearest_hundred = 'round_off_to_nearest_hundred' $get_round_off_to_nearest_hundred = false $round_off_to_nearest_thousand = 'round_off_to_nearest_thousand' $get_round_off_to_nearest_thousand = false $change_12_to_24 = 'change_12h_to_24h' $get_12_to_24 = false $change_24_to_12 = 'change_24h_to_12h' $get_24_to_12 = false $get_factors = 'get_factors' $get_factors_nnt = false $get_common_factors = 'get_common_factors' $get_common_factors_nnt = false $get_multiples = 'get_multiples' $get_multiples_23916 = false $get_add_or_minus_multiples = 'add_or_minus_multiples' $add_or_minus_multiples_23916 = false $get_common_numbers = 'get_common_numbers' $get_common_numbers_240916 = false $substr_array_singular = 'array_singular' $array_singular_101016 = false $substr_array_plural = 'array_plural' $array_plural_101016 = false $substr_print_fraction = 'print_fraction' $print_fraction_101016 = false $substr_array_capitalize = 'array_capitalize' $array_capitalize_101016 = false $substr_array_get_words = 'array_get_words' $array_get_words_31316 = false $substr_array_get_1st_letter = 'array_get_1st_letter' $array_array_get_1st_letter = false $substr_array_get_next_loop = 'array_get_next_loop' $array_get_next_loop = false $substr_array_get_next_break = 'array_get_next_break' $array_get_next_break = false $substr_multiply_fraction = 'do_fraction' $array_multiply_fraction = (int) 0 $substr_change_to_italic = 'change_to_italic' $array_change_to_italic = false $match = array( (int) 0 => 'print_fraction(45,150)', (int) 1 => '45,150', (int) 2 => ')' ) $count_check = array( (int) 0 => '+', (int) 1 => '0,3/10' ) $arr_caculoid = array( (int) 0 => '+', (int) 1 => '-', (int) 2 => '*', (int) 3 => '/' ) $two_fraction = array( (int) 0 => '0', (int) 1 => '3/10' ) $findme2 = '.' $search_tu = false $search_tu2 = false $search_mau = (int) 1 $search_mau2 = false $tuOne = '0' $mauOne = (int) 1 $split_mau = array( (int) 0 => '3', (int) 1 => '10' ) $tuTwo = '3' $mauTwo = '10' $k1 = (int) 29 $v1 = ''CommonComponent::generateAdvClone() - APP/Controller/Component/CommonComponent.php, line 4567 ClonesController::index2() - APP/Controller/ClonesController.php, line 2226 ReflectionMethod::invokeArgs() - [internal], line ?? Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167 [main] - APP/webroot/index.php, line 119
Notice (8): Undefined variable: mauMain [APP/Controller/Component/CommonComponent.php, line 4567]Code Context$giatri = $tuMain/$mauMain;
}else{
$giatri = $tuMain.'/'.$mauMain;
$clone = array( 'id' => '15402', 'chart' => '', 'question_id' => '44163', 'clone_type' => '1', 'phpfile' => null, 'clone_symbol' => null, 'clone_content' => '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>', 'clone_solution_step' => '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h', 'clone_answer' => '(a) 0$(t8) $(m10); (b) $(n20) km/h ', 'array' => object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} }, 'clone_image' => null, 'clone_solution_step_image' => null, 'clone_answer_image' => null, 'status' => true, 'created' => '2019-09-08 23:34:33', 'modified' => '2019-09-09 10:39:12', 'original_question' => 'Kenny and Jerry started on a 50-kim cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 40 km, Kenny cycled faster than Jerry. He arrived at the fining point 40 minutes before Jerry who was 10 km behind him. Jerry did not change his speed throughout and completed it at 11 30. <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was Kenny's average speed for the remaining 40 km of the trip in km/h?</li> </ol>', 'formula' => array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ), 'time_value' => array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ), 'criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'type_criterion' => array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ), 'image_gridline' => '', 'code_gridline' => '', 'level' => '', 'topic_id' => '', 'source' => '', 'question_code' => 'P6.SP.JC.19090801-A1', 'tag' => '', 'mark' => '', 'text_working' => '["","","","","","","","","","","","","","","\/\/","","","","","","","","","","","$(n40) \u00f7 $(h2) = $(n20)","","","",""]', 'original_solution' => '(a)<br /> Jerry's average speed<br /> = 10 ÷ <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 15 km/h<br /> <br /> Time that Jerry took for the trip<br /> = 50 ÷ 15<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h<br /> <br /> 3 <span class="frac"><sup>1</sup><sub>3</sub></span> h before 11 30 is 08 10.<br /> <br /> (b)<br /> Time that Kenny took for the remaining 40 km of the trip<br /> = 3 <span class="frac"><sup>1</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span> - <span class="frac"><sup>2</sup><sub>3</sub></span><br /> = 2 h<br /> <br /> Kenny's average speed<br /> = 40 ÷ 2<br /> = 20 km/h<br /> <br /> Answer(s): (a) 08 10; (b) 20 km/h', 'delete_by' => null, 'delete_date' => null ) $Array1 = object(Array1) { table => 'array1s' validate => array() useDbConfig => 'default' useTable => 'array1s' id => '61' data => array() schemaName => 'ischoolb_orgi' primaryKey => 'id' validationErrors => array() validationDomain => null tablePrefix => '' plugin => null name => 'Array1' alias => 'Array1' tableToModel => array( 'array1s' => 'Array1' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => array( 'id' => array( [maximum depth reached] ), 'name' => array( [maximum depth reached] ), 'content' => array( [maximum depth reached] ), 'note' => array( [maximum depth reached] ), 'created' => array( [maximum depth reached] ), 'modified' => array( [maximum depth reached] ) ) [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => true [protected] _eventManager => object(CakeEventManager) {} [protected] _validator => null } $Prime = object(AppModel) { useDbConfig => 'default' useTable => 'primes' id => false data => array() schemaName => null table => 'primes' primaryKey => 'id' validate => array() validationErrors => array() validationDomain => null plugin => null name => 'Prime' alias => 'Prime' tableToModel => array( 'primes' => 'Prime' ) cacheQueries => false belongsTo => array() hasOne => array() hasMany => array() hasAndBelongsToMany => array() actsAs => null Behaviors => object(BehaviorCollection) {} whitelist => array() cacheSources => true findQueryType => null recursive => (int) 1 order => null virtualFields => array() __backAssociation => array() __backInnerAssociation => array() __backOriginalAssociation => array() __backContainableAssociation => array() __safeUpdateMode => false useConsistentAfterFind => true findMethods => array( 'all' => true, 'first' => true, 'count' => true, 'neighbors' => true, 'list' => true, 'threaded' => true ) [protected] _schema => null [protected] _associationKeys => array( 'belongsTo' => array( [maximum depth reached] ), 'hasOne' => array( [maximum depth reached] ), 'hasMany' => array( [maximum depth reached] ), 'hasAndBelongsToMany' => array( [maximum depth reached] ) ) [protected] _associations => array( (int) 0 => 'belongsTo', (int) 1 => 'hasOne', (int) 2 => 'hasMany', (int) 3 => 'hasAndBelongsToMany' ) [protected] _insertID => null [protected] _sourceConfigured => false [protected] _eventManager => null [protected] _validator => null } $answer_fix = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $count_crition = (int) 51 $count_array_break = (int) 0 $count_variable_nnt = (int) 0 $message_nnt = '' $field = 'time_value' $array_get = array( (int) 0 => 'n10', (int) 8 => 'n50', (int) 9 => 'n50', (int) 6 => 'n10', (int) 2 => 't40', (int) 14 => 'h11', (int) 18 => 'm30', (int) 1 => '(n40)', (int) 25 => '(n40)', (int) 3 => '(t60)', (int) 4 => '(st60)', (int) 5 => '(st60)', (int) 22 => '(st60)', (int) 7 => '(n15)', (int) 10 => '(n15)', (int) 28 => '(n15)', (int) 20 => '(h3)', (int) 21 => '(h3)', (int) 11 => '(z)', (int) 12 => '(sz)', (int) 13 => '(sz)', (int) 15 => '(t1)', (int) 16 => '(w)', (int) 17 => '(w)', (int) 19 => '(m10)' ) $tempt = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $list_name_array = array( (int) 0 => 'Julian', (int) 1 => 'Brandon' ) $list_array_item = array( 'Jerry' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 5, 'manyArray' => '1', 'capitalize' => '0' ), 'Kenny' => array( 'listArray' => array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ), 'keyArray' => (int) 12, 'manyArray' => '1', 'capitalize' => '0' ) ) $list_italic = array() $array_variable = object(stdClass) { 1567994569673 => object(stdClass) {} 1567994633770 => object(stdClass) {} 1567957317267 => object(stdClass) {} 1567957684514 => object(stdClass) {} 1567994682256 => object(stdClass) {} 1567995993397 => object(stdClass) {} 1567995994231 => object(stdClass) {} } $question_content = '$(Kenny) and $(Jerry) started on a $(n50)-km cycling trip at the same time. They cycled at the same speed for first $(n10) km. For the remaining $(n40) km, $(Kenny) cycled faster than $(Jerry). He arrived at the finishing point $(t40) minutes before $(Jerry) who was $(n10) km behind him. $(Jerry) did not change his speed throughout and completed it at 0$(h11) $(m30).<br /> <ol> <li>At what time did the trip begin? Give the answer in 12-hour format.</li> <li>What was $(Kenny)'s average speed for the remaining $(n40) km of the trip in km/h?</li> </ol>' $solution_step = '(a)<br />60 min = 1 h<br />$(t40) min =<span class="frac"><sup>$(t40)</sup><sub>60</sub></span> h = <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> <br /><br />$(Jerry)'s average speed<br /> = $(n10) ÷ <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(n15) km/h<br /> <br /> Time that $(Jerry) took for the trip<br /> = $(n50) ÷ $(n15)<br />= $(h3)$(z) h<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> h<br />= $(h3) h $(w) min<br /> <br />$(h3) h $(w) min before 0$(h11) $(m30) is 0$(t8) $(m10).<br /> <br /> (b)<br />To find the time that $(Kenny) took for the remaining $(n40) km of the trip, we need to use the time that $(Jerry) took subtract that of the time taken for first $(n10) km and the time that $(Kenny) was faster than $(Jerry).<br /><br /> Time that $(Kenny) took for the remaining $(n40) km of the trip<br /> = $(h3)<span class="frac"><sup>$(t1)</sup><sub>$(t3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span> - <span class="frac"><sup>$(tt2)</sup><sub>$(tt3)</sub></span><br /> = $(h2) h<br /> <br /> $(Kenny)'s average speed<br /> = $(n40) ÷ $(h2)<br /> = $(n20) km/h<br /> <br /> Answer(s): (a) 0$(t8) $(m10); (b) $(n20) km/h' $clone_answer = '(a) 0$(t8) $(m10); (b) $(n20) km/h ' $formula = array( (int) 0 => '45-15=30', (int) 1 => 'if(more_than(30>20))continue', (int) 2 => 'print_fraction(6,60)=6/60', (int) 3 => 'simplify_fraction(6/60)=1/10', (int) 4 => 'get_numerator(1/10)=1', (int) 5 => 'get_denominator(1/10)=10', (int) 6 => '15/1*10=150', (int) 7 => 'if(whole_number(150))continue', (int) 8 => 'get_quotient(45,150)=0', (int) 9 => 'get_remainder(45,150)=45', (int) 10 => 'print_fraction(45,150)=45/150', (int) 11 => 'simplify_fraction(45/150)=3/10', (int) 12 => 'get_numerator(3/10)=3', (int) 13 => 'get_denominator(3/10)=10', (int) 14 => '7-0=7', (int) 15 => '3/10*60=18', (int) 16 => 'if(more_than(18>9))continue', (int) 17 => 'if(whole_number(18))continue', (int) 18 => '30-18=12', (int) 19 => 'if(more_than(12>9))continue', (int) 20 => 'do_fraction(+:0,3/10)=$(hw)', (int) 21 => 'if(more_than(0>0))continue', (int) 22 => 'do_fraction(+:1/10,1/10)=$(2sz)', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2)', (int) 24 => 'if(more_than($(h2)>1))continue', (int) 25 => 'do_fraction(/:30,$(h2))=$(n20s)', (int) 26 => 'simplify_fraction($(n20s))=$(n20)', (int) 27 => 'if(more_than($(n20)>35))back', (int) 28 => 'if(more_than($(n20)>150))continue', (int) 29 => '' ) $formula_1 = array( (int) 0 => '$(n50)-$(n10)=$(n40)', (int) 1 => 'if(more_than($(n40)>20)) continue', (int) 2 => 'print_fraction($(t40),60)=$(t60) ', (int) 3 => 'simplify_fraction($(t60))=$(st60) ', (int) 4 => 'get_numerator($(st60))=$(tt2) ', (int) 5 => 'get_denominator($(st60))=$(tt3) ', (int) 6 => '$(n10)/$(tt2)*$(tt3)=$(n15)', (int) 7 => 'if(whole_number($(n15))) continue', (int) 8 => 'get_quotient($(n50),$(n15))=$(h3) ', (int) 9 => 'get_remainder($(n50),$(n15))=$(r3) ', (int) 10 => 'print_fraction($(r3),$(n15))=$(z) ', (int) 11 => 'simplify_fraction($(z))=$(sz) ', (int) 12 => 'get_numerator($(sz))=$(t1) ', (int) 13 => 'get_denominator($(sz))=$(t3) ', (int) 14 => '$(h11)-$(h3)=$(t8)', (int) 15 => '$(t1)/$(t3)*60=$(w)', (int) 16 => 'if(more_than($(w)>9)) continue', (int) 17 => 'if(whole_number($(w))) continue', (int) 18 => '$(m30)-$(w)=$(m10)', (int) 19 => 'if(more_than($(m10)>9)) continue', (int) 20 => 'do_fraction(+:$(h3),$(sz))=$(hw) ', (int) 21 => 'if(more_than($(h3)>0)) continue', (int) 22 => 'do_fraction(+:$(st60),$(st60))=$(2sz) ', (int) 23 => 'do_fraction(-:$(hw),$(2sz))=$(h2) ', (int) 24 => 'if(more_than($(h2)>1)) continue', (int) 25 => 'do_fraction(/:$(n40),$(h2))=$(n20s) ', (int) 26 => 'simplify_fraction($(n20s))=$(n20) ', (int) 27 => 'if(more_than($(n20)>35)) back', (int) 28 => 'if(more_than($(n20)>$(n15))) continue', (int) 29 => '' ) $criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $type_criterion = array( (int) 0 => '', (int) 1 => '', (int) 2 => '', (int) 3 => '', (int) 4 => '', (int) 5 => '', (int) 6 => '', (int) 7 => '', (int) 8 => '', (int) 9 => '', (int) 10 => '', (int) 11 => '', (int) 12 => '', (int) 13 => '', (int) 14 => '', (int) 15 => '', (int) 16 => '', (int) 17 => '', (int) 18 => '', (int) 19 => '', (int) 20 => '', (int) 21 => '', (int) 22 => '', (int) 23 => '', (int) 24 => '', (int) 25 => '', (int) 26 => '', (int) 27 => '', (int) 28 => '', (int) 29 => '' ) $time_value = array( (int) 0 => '1567956325806', (int) 1 => '1567994704507', (int) 2 => '1567957190303', (int) 3 => '1567957218666', (int) 4 => '1567957359423', (int) 5 => '1567957392416', (int) 6 => '1567957818212', (int) 7 => '1567994855125', (int) 8 => '1567958092589', (int) 9 => '1567958093258', (int) 10 => '1567958147508', (int) 11 => '1567958180968', (int) 12 => '1567958459449', (int) 13 => '1567958460096', (int) 14 => '1567958510560', (int) 15 => '1567958667042', (int) 16 => '1567994759217', (int) 17 => '1567994932721', (int) 18 => '1567958770962', (int) 19 => '1567994812657', (int) 20 => '1567994100663', (int) 21 => '1567994826916', (int) 22 => '1567994169469', (int) 23 => '1567994132128', (int) 24 => '1567996310765', (int) 25 => '1567994167512', (int) 26 => '1567995106038', (int) 27 => '1567994133018', (int) 28 => '1567995033025', (int) 29 => '1567996295687' ) $k = '1567995994231' $v = object(stdClass) { cate => 'items' name => 'Kenny' range => '61' attr => object(stdClass) {} } $array_system = array( (int) 0 => 'Caden', (int) 1 => 'Luis', (int) 2 => 'Vaidev', (int) 3 => 'Archie', (int) 4 => 'Cole', (int) 5 => 'Julian', (int) 6 => 'Jeremy', (int) 7 => 'Seth', (int) 8 => 'Pierre', (int) 9 => 'Japheth', (int) 10 => 'Neave', (int) 11 => 'Jenson', (int) 12 => 'Brandon', (int) 13 => 'Tom', (int) 14 => 'Ahmad', (int) 15 => 'Bryan', (int) 16 => 'Ryan', (int) 17 => 'Asher', (int) 18 => 'Ben', (int) 19 => 'Carl', (int) 20 => 'David', (int) 21 => 'Ethan', (int) 22 => 'Fred', (int) 23 => 'George', (int) 24 => 'Henry', (int) 25 => 'Ian', (int) 26 => 'Jack', (int) 27 => 'Ken', (int) 28 => 'Liam', (int) 29 => 'Mark', (int) 30 => 'Nick', (int) 31 => 'Oscar', (int) 32 => 'Peter', (int) 33 => 'Rael', (int) 34 => 'Sean', (int) 35 => 'Tim', (int) 36 => 'Vincent', (int) 37 => 'Will', (int) 38 => 'Xavier', (int) 39 => 'Zane', (int) 40 => 'Albert', (int) 41 => 'Andy', (int) 42 => 'Bobby', (int) 43 => 'Billy', (int) 44 => 'Charlie', (int) 45 => 'Cody', (int) 46 => 'Daniel', (int) 47 => 'Dylan', (int) 48 => 'Eric', (int) 49 => 'Elijah', (int) 50 => 'Fabian', (int) 51 => 'Flynn', (int) 52 => 'Gabriel', (int) 53 => 'Glen', (int) 54 => 'Harry', (int) 55 => 'Howard', (int) 56 => 'Ivan', (int) 57 => 'John', (int) 58 => 'Justin', (int) 59 => 'Luke', (int) 60 => 'Lee', (int) 61 => 'Michael', (int) 62 => 'Owen', (int) 63 => 'Oliver', (int) 64 => 'Paul', (int) 65 => 'Perry', (int) 66 => 'Riordan', (int) 67 => 'Reggie', (int) 68 => 'Sam', (int) 69 => 'Simon', (int) 70 => 'Tommy', (int) 71 => 'Valen', (int) 72 => 'Wesley', (int) 73 => 'Warren', (int) 74 => 'Zeph' ) $dem_array_trung = (int) 1 $value_rand_check = (int) 12 $value_check = 'Brandon' $tempt_array = array( (int) 0 => '10', (int) 1 => '15', (int) 2 => '20', (int) 3 => '25', (int) 4 => '30' ) $tempt_k = (int) 4 $tempt_v = '30' $check_who_nnt = (int) 0 $from = '7' $to = '9' $findme = '/' $arr_variable = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon', '(n40)' => (int) 30, '(t60)' => '6/60', '(st60)' => '1/10', '(tt2)' => (int) 1, '(tt3)' => (int) 10, '(n15)' => (int) 150, '(h3)' => '0', '(r3)' => '45', '(z)' => '45/150', '(sz)' => '3/10', '(t1)' => (int) 3, '(t3)' => (int) 10, '(t8)' => (int) 7, '(w)' => (float) 18, '(m10)' => (int) 12 ) $variable_k = '(m10)' $variable_v = '12' $formula_k = (int) 20 $formula_v = 'do_fraction(+:$(h3),$(sz))=$(hw)' $criterion_k = (int) 29 $criterion_v = '' $type_criterion_k = (int) 29 $type_criterion_v = '' $variable_show = array( 'n50' => '45', 'n10' => '15', 't40' => '6', 'h11' => (int) 7, 'm30' => '30', 'Jerry' => 'Julian', 'Kenny' => 'Brandon' ) $start = 'do_fraction(' $end = ')' $array_mixed_nnt = array() $check_changes = '' $criterion_continue = '))=$(hw)' $criterion_back = '(hw)' $type_criterion_action = (int) 1 $get_between = '+:0,3/10' $type_cri = 'more_than' $get_between_value = '12>9' $bieuthuc = array( (int) 0 => 'do_fraction(+:0,3/10)', (int) 1 => '(hw)' ) $substr_pos = 'change_decimal_to_fraction' $get_numerator = false $get_whole_number_nnt = false $pos = false $giatri = '' $substr_simplify_frac = 'simplify_fraction' $simplify_frac = false $substr_simplify_ratio = 'simplify_ratio' $simplify_ratio = false $substr_get_element_of_ratio = 'get_element' $get_element_of_ratio = false $substr_numberto2decimal = 'change_number_to_2dp' $change_to_2dp = false $substr_digit_5_0 = 'change_to_2dp_with_5_or_0' $change_to_2dp_5_or_0 = false $substr_mixed_num = 'change_improper_to_mixed_number' $mixed_num = false $substr_mixed_to_improper = 'change_mixed_number_to_improper' $mixed_to_improper = false $substr_invert_fraction = 'invert_fraction' $invert_fraction = false $substr_get_same_numerator = 'share_same_numerator' $get_same_numerator = false $substr_get_same_denominator = 'share_same_denominator' $get_same_denominator = false $substr_reduce_into_ratio = 'simplify_any_into_ratio' $reduce_into_ratio = false $substr_multiply_subscript = 'multiply_ratio_subscript' $multiply_subscript = false $substr_assign = 'assign' $assign = false $substr_is_12_hour_time_am_pm = 'get_12_hour_time_am_pm' $is_12_hour_time_am_pm = false $substr_is_2400_hour_time = 'get_2400_hour_time' $is_2400_hour_time = false $substr_add_or_minus_time = 'add_or_minus_min_or_s' $add_or_minus_time = false $substr_change_percentage_to_frac = 'change_percentage_to_frac' $change_percentage_to_frac = false $substr_round_2_decimal = 'round_2_decimal_place' $round_2_decimal_place = false $substr_round_1_decimal = 'round_1_decimal_place' $round_1_decimal_place = false $substr_get_quotient = 'get_quotient' $get_quotient = false $substr_get_remainder = 'get_remainder' $get_remainder = false $substr_change_min_to_hour_min = 'change_min_to_h_min' $change_min_to_hour_min = false $substr_change_h_min_to_min = 'change_h_min_to_min' $change_h_min_to_min = false $substr_carry_1 = 'carry_1_from_mixed_number' $get_carry_1 = false $change_d_or_p_to_fraction = 'change_to_unsimplied_fraction' $get_change_d_or_p_to_fraction = false $round_off_to_nearest_ten = 'round_off_to_nearest_ten' $get_round_off_to_nearest_ten = false $round_off_to_nearest_hundred = 'round_off_to_nearest_hundred' $get_round_off_to_nearest_hundred = false $round_off_to_nearest_thousand = 'round_off_to_nearest_thousand' $get_round_off_to_nearest_thousand = false $change_12_to_24 = 'change_12h_to_24h' $get_12_to_24 = false $change_24_to_12 = 'change_24h_to_12h' $get_24_to_12 = false $get_factors = 'get_factors' $get_factors_nnt = false $get_common_factors = 'get_common_factors' $get_common_factors_nnt = false $get_multiples = 'get_multiples' $get_multiples_23916 = false $get_add_or_minus_multiples = 'add_or_minus_multiples' $add_or_minus_multiples_23916 = false $get_common_numbers = 'get_common_numbers' $get_common_numbers_240916 = false $substr_array_singular = 'array_singular' $array_singular_101016 = false $substr_array_plural = 'array_plural' $array_plural_101016 = false $substr_print_fraction = 'print_fraction' $print_fraction_101016 = false $substr_array_capitalize = 'array_capitalize' $array_capitalize_101016 = false $substr_array_get_words = 'array_get_words' $array_get_words_31316 = false $substr_array_get_1st_letter = 'array_get_1st_letter' $array_array_get_1st_letter = false $substr_array_get_next_loop = 'array_get_next_loop' $array_get_next_loop = false $substr_array_get_next_break = 'array_get_next_break' $array_get_next_break = false $substr_multiply_fraction = 'do_fraction' $array_multiply_fraction = (int) 0 $substr_change_to_italic = 'change_to_italic' $array_change_to_italic = false $match = array( (int) 0 => 'print_fraction(45,150)', (int) 1 => '45,150', (int) 2 => ')' ) $count_check = array( (int) 0 => '+', (int) 1 => '0,3/10' ) $arr_caculoid = array( (int) 0 => '+', (int) 1 => '-', (int) 2 => '*', (int) 3 => '/' ) $two_fraction = array( (int) 0 => '0', (int) 1 => '3/10' ) $findme2 = '.' $search_tu = false $search_tu2 = false $search_mau = (int) 1 $search_mau2 = false $tuOne = '0' $mauOne = (int) 1 $split_mau = array( (int) 0 => '3', (int) 1 => '10' ) $tuTwo = '3' $mauTwo = '10' $k1 = (int) 29 $v1 = ''CommonComponent::generateAdvClone() - APP/Controller/Component/CommonComponent.php, line 4567 ClonesController::index2() - APP/Controller/ClonesController.php, line 2226 ReflectionMethod::invokeArgs() - [internal], line ?? Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490 Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 193 Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 167 [main] - APP/webroot/index.php, line 119
The reports are available for Premium members only.
Why use limited features when you can enjoy full features and excel in Math?
There’s no risk. Cancel any time.
Let's start my subscription now.
When you click the Next button, you will be given 1-minute grace period to decide whether to do the next question type.
The question will be marked as incorrect if you exceed 1 minute and leave the question page.
Click the Back button instead if you would like to return to the topic page.
Date:18 May 2024
Topic:SPEED
Question Number:P6.SP.JC.19090801-A1
Student:
Class:
Level:
School:
A password link has been sent to the Child's Email:
Please click the link to reset the Child's Password.