City A and City B were 539 km apart. A van travelled from City A towards City B. At the same time, a lorry started from City B to City A. After travelling 1
12 h, the two vehicles were still 308 km apart. If the ratio of the average speed of the lorry to that of the van was 5 : 6, 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
12 h by the two vehicles
= 539 - 308
= 231 km
Combined speed of the two vehicles
= 231 ÷
32 = 231 x
23 = 154 km/h
Average speed of the lorry : Average speed of the van = 5 : 6
5 u + 6 u = 11 u
11 u = 154
1 u = 154 ÷ 11 = 14
Average speed of the van
= 6 u
= 6 x 14
= 84 km/h
(b)
Time taken for the lorry and the van to meet travelling the rest of the journey
= 308 ÷ 154
= 2 h
Answer(s): (a) 84 km/h; (b) 2 h