City H and City J were 390 km apart. A van travelled from City H towards City J. At the same time, a bus started from City J to City H. After travelling 1
13 h, the two vehicles were still 234 km apart. If the ratio of the average speed of the bus to that of the van 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 bus : Average speed of the van = 4 : 5
4 u + 5 u = 9 u
9 u = 117
1 u = 117 ÷ 9 = 13
Average speed of the van
= 5 u
= 5 x 13
= 65 km/h
(b)
Time taken for the bus and the van to meet travelling the rest of the journey
= 234 ÷ 117
= 2 h
Answer(s): (a) 65 km/h; (b) 2 h