City X and City Y were 520 km apart. A car travelled from City X towards City Y. At the same time, a van started from City Y to City X. After travelling 1
13 h, the two vehicles were still 312 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 car.
- the time taken for them to meet travelling the rest of the journey. Express your answer in h.
(a)
Distance covered in 1
13 h by the two vehicles
= 520 - 312
= 208 km
Combined speed of the two vehicles
= 208 ÷
43 = 208 x
34 = 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 car
= 7 u
= 7 x 12
= 84 km/h
(b)
Time taken for the van and the car to meet travelling the rest of the journey
= 312 ÷ 156
= 2 h
Answer(s): (a) 84 km/h; (b) 2 h