City G and City H were 390 km apart. A car travelled from City G towards City H. At the same time, a van started from City H to City G. After travelling 1
12 h, the two vehicles were still 156 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
= 390 - 156
= 234 km
Combined speed of the two vehicles
= 234 ÷
32 = 234 x
23 = 156 km/h
Average speed of the van : Average speed of the car = 6 : 7
6 u + 7 u = 13 u
13 u = 156
1 u = 156 ÷ 13 = 12
Average speed of the van
= 6 u
= 6 x 12
= 72 km/h
(b)
Time taken for the van and the car to meet travelling the rest of the journey
= 156 ÷ 156
= 1 h
Answer(s): (a) 72 km/h; (b) 1 h