City K and City L were 770 km apart. A van travelled from City K towards City L. At the same time, a lorry started from City L to City K. After travelling 1
23 h, the two vehicles were still 495 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
23 h by the two vehicles
= 770 - 495
= 275 km
Combined speed of the two vehicles
= 275 ÷
53 = 275 x
35 = 165 km/h
Average speed of the lorry : Average speed of the van = 5 : 6
5 u + 6 u = 11 u
11 u = 165
1 u = 165 ÷ 11 = 15
Average speed of the van
= 6 u
= 6 x 15
= 90 km/h
(b)
Time taken for the lorry and the van to meet travelling the rest of the journey
= 495 ÷ 165
= 3 h
Answer(s): (a) 90 km/h; (b) 3 h