31 P6.SP.TL.18012282
Level 3
Building A and Building B were 360 km apart. A car travelled from Building A towards Building B. At the same time, a bus started from Building B to Building A. After travelling 112 hours, the two vehicles were still 144 km apart. If the ratio of the average speed of the bus to that of the car was 4 : 5, find
  1. the average speed of the bus.
  2. the time taken for them to meet. travelling the rest of the journey
4 m
DST triangle Average speed Different starting point Same starting time Distance apart Direct ratio Common time Duration Units method
32 P6.SP.TL.18012288
Level 3
Andy and Benny were planning to run on a circular track with a circumference of 400 m. Both of them started jogging together at the same start point and moved round the track in a clockwise direction at uniform speeds. Andy completed a full round in 50 s. Benny completed a full round in 40 s.
  1. How long would it take for Benny to overtake Andy for the first time?
  2. How far was Benny ahead of Andy after 10 s?
4 m
DST triangle Same starting point Distance apart Overtaking Circular track Duration LCM
33 P6.SP.TL.18012289
Level 3
Shan and Ella started off at the same spot and ran at average speeds round a 3-km circular path. Shan took 15 minutes to complete each round. Ella completed each round in 20 minutes.
  1. How far ahead of Ella would Shan be after 1 minute? Express the answer in metres.
  2. How long would it take Shan to meet Ella for the first time?
  3. How many rounds would Shan have completed by then?
4 m
DST triangle Same starting point Meeting point Distance apart Circular track Unit conversion Duration LCM
34 P6.AP.TL.17090818
Level 3
The figure is not drawn to scale. Two balls, X and Y, turn and move along the line AB in opposite directions. The radius of X is 10 cm. The ratio of the diameter of Ball X to that of Ball Y is 5 : 2. If Ball X turns 10 rounds and Ball Y turns 2 rounds, how far apart are the centres of the balls? (Take π = 3.14)
4 m
Circle Circumference Ratio to units Distance apart
35 P6.SP.TL.18012295
Level 3
Ray left City B for City A at 07 30. Lindy left City B for City C at the same time. At 10 30, they were 480 km apart. Both maintained a constant speed and reached their destination at the same time at 12 00 h.
  1. Find the distance between Cities A and C.
  2. If Lindy's speed was 35 the speed of Fred, find Ray's speed.
5 m
DST triangle Average speed Same starting time Opposite direction Distance apart Direct ratio Common time Units method
36 P6.SP.TL.18012292
Level 3
City X and City Y are 420 km apart. At 3.45 p.m., Joni is travelling at a uniform speed left City X for City Y while Ben set off from City Y to City X along the same road at a uniform speed, which was 12 km/h slower than that of Joni. The two met at 6.45 p.m.
  1. Find the speed of Joni.
  2. If Ben continued to travel at the same speed, how long would it take for him to reach his destination after the two met? Express the answer in mixed number.
5 m
DST triangle Average speed Different speed Different starting point Same starting time Meeting point Distance apart Duration Common time More than or less than
37 P6.AP.TL.17090842
Level 3
This figure is not drawn to scale. Wheel A and Wheel B are touching a vertical plastic sheet. The ratio of the radius of the small wheel A to the radius of the big wheel B is 2 : 5. The total radii of Wheel A and Wheel B is 196 cm. Both wheels are rolled out in opposite direction shown until they are 2660 cm apart. The two wheels need to make the same number of revolutions. How many revolutions does each wheel make assuming that each wheel must make a complete revolution? (Take π = 227)
5 m
Circumference Ratio to units Distance apart Equal stage Units method

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