City K and City L were 845 km apart. A sports car travelled from City K towards City L. At the same time, a van started from City L to City K. After travelling 1
13 h, the two vehicles were still 585 km apart. If the ratio of the average speed of the van to that of the sports car was 6 : 7, find
- the average speed of the sports 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
= 845 - 585
= 260 km
Combined speed of the two vehicles
= 260 ÷
43 = 260 x
34 = 195 km/h
Average speed of the van : Average speed of the sports car = 6 : 7
6 u + 7 u = 13 u
13 u = 195
1 u = 195 ÷ 13 = 15
Average speed of the sports car
= 7 u
= 7 x 15
= 105 km/h
(b)
Time taken for the van and the sports car to meet travelling the rest of the journey
= 585 ÷ 195
= 3 h
Answer(s): (a) 105 km/h; (b) 3 h