City R and City S are 363 km apart. At 3.37 p.m., Tommy is travelling at a uniform speed left City R for City S while Luke set off from City S to City R along the same road at a uniform speed, which was 7 km/h slower than that of Tommy. The two met at 6.37 p.m.
- Find the speed of Tommy.
- If Luke continued to travel at the same speed, how long would it take for him to reach his destination after the two met? Express your answer in mixed number.
(a)
Time taken for Tommy and Luke to travel from 3.37 p.m. to 6.37 p.m. = 3 h
Average speed of Tommy and Luke
= 363 ÷ 3
= 121 km/h
Tommy's speed
= (121 + 7) ÷ 2
= 128 ÷ 2
= 64 km/h
(b)
Luke's speed
= 64 - 7
= 57 km/h
Distance that Luke travelled in 3 h
= 3 x 57
= 171 km
Remaining distance that Luke needed to travel
= 363 - 171
= 192 km
Time that Luke needed to reach his destination after the two met
= 192 ÷ 57
= 3
2157 = 3
719 h
Answer(s): (a) 64 km/h; (b) 3
719 h