City W and City X were 770 km apart. A car travelled from City W towards City X. At the same time, a van started from City X to City W. After travelling 1
23 h, the two vehicles were still 495 km apart. If the ratio of the average speed of the van to that of the car 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 van : Average speed of the car = 5 : 6
5 u + 6 u = 11 u
11 u = 165
1 u = 165 ÷ 11 = 15
Average speed of the van
= 5 u
= 5 x 15
= 75 km/h
(b)
Time taken for the van and the car to meet travelling the rest of the journey
= 495 ÷ 165
= 3 h
Answer(s): (a) 75 km/h; (b) 3 h