City H and City J are 387 km apart. At 6.21 p.m., Howard is travelling at a uniform speed left City H for City J while Peter set off from City J to City H along the same road at a uniform speed, which was 9 km/h slower than that of Howard. The two met at 9.21 p.m.
- Find the speed of Howard.
- If Peter 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 Howard and Peter to travel from 6.21 p.m. to 9.21 p.m. = 3 h
Average speed of Howard and Peter
= 387 ÷ 3
= 129 km/h
Howard's speed
= (129 + 9) ÷ 2
= 138 ÷ 2
= 69 km/h
(b)
Peter's speed
= 69 - 9
= 60 km/h
Distance that Peter travelled in 3 h
= 3 x 60
= 180 km
Remaining distance that Peter needed to travel
= 387 - 180
= 207 km
Time that Peter needed to reach his destination after the two met
= 207 ÷ 60
= 3
2760 = 3
920 h
Answer(s): (a) 69 km/h; (b) 3
920 h