City N and City P were 507 km apart. A car travelled from City N towards City P. At the same time, a van started from City P to City N. After travelling 1
13 h, the two vehicles were still 351 km apart. If the ratio of the average speed of the van to that of the 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
= 507 - 351
= 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 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 car to meet travelling the rest of the journey
= 351 ÷ 117
= 3 h
Answer(s): (a) 52 km/h; (b) 3 h