City A and City B were 390 km apart. A sports car travelled from City A towards City B. At the same time, a van started from City B to City A. After travelling 1
13 h, the two vehicles were still 234 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
13 h by the two vehicles
= 390 - 234
= 156 km
Combined speed of the two vehicles
= 156 ÷
43 = 156 x
34 = 117 km/h
Average speed of the van : Average speed of the sports car = 4 : 5
4 u + 5 u = 9 u
9 u = 117
1 u = 117 ÷ 9 = 13
Average speed of the van
= 4 u
= 4 x 13
= 52 km/h
(b)
Time taken for the van and the sports car to meet travelling the rest of the journey
= 234 ÷ 117
= 2 h
Answer(s): (a) 52 km/h; (b) 2 h