City R and City S were 612 km apart. A car travelled from City R towards City S. At the same time, a van started from City S to City R. After travelling 1
14 h, the two vehicles were still 432 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
14 h by the two vehicles
= 612 - 432
= 180 km
Combined speed of the two vehicles
= 180 ÷
54 = 180 x
45 = 144 km/h
Average speed of the van : Average speed of the 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 car to meet travelling the rest of the journey
= 432 ÷ 144
= 3 h
Answer(s): (a) 64 km/h; (b) 3 h