City X and City Y were 684 km apart. A sports car travelled from City X towards City Y. At the same time, a van started from City Y to City X. After travelling 1
34 h, the two vehicles were still 432 km apart. If the ratio of the average speed of the van to that of the sports car was 4 : 5, find
- the average speed of the van.
- the time taken for them to meet travelling the rest of the journey. Express your answer in h.
(a)
Distance covered in 1
34 h by the two vehicles
= 684 - 432
= 252 km
Combined speed of the two vehicles
= 252 ÷
74 = 252 x
47 = 144 km/h
Average speed of the van : Average speed of the sports car = 4 : 5
4 u + 5 u = 9 u
9 u = 144
1 u = 144 ÷ 9 = 16
Average speed of the van
= 4 u
= 4 x 16
= 64 km/h
(b)
Time taken for the van and the sports car to meet travelling the rest of the journey
= 432 ÷ 144
= 3 h
Answer(s): (a) 64 km/h; (b) 3 h