City U and City V were 819 km apart. A car travelled from City U towards City V. At the same time, a van started from City V to City U. After travelling 1
12 h, the two vehicles were still 546 km apart. If the ratio of the average speed of the van to that of the car was 6 : 7, 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
= 819 - 546
= 273 km
Combined speed of the two vehicles
= 273 ÷
32 = 273 x
23 = 182 km/h
Average speed of the van : Average speed of the car = 6 : 7
6 u + 7 u = 13 u
13 u = 182
1 u = 182 ÷ 13 = 14
Average speed of the van
= 6 u
= 6 x 14
= 84 km/h
(b)
Time taken for the van and the car to meet travelling the rest of the journey
= 546 ÷ 182
= 3 h
Answer(s): (a) 84 km/h; (b) 3 h