City K and City L were 385 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 165 km apart. If the ratio of the average speed of the van to that of the sports car was 5 : 6, 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
= 385 - 165
= 220 km
Combined speed of the two vehicles
= 220 ÷
43 = 220 x
34 = 165 km/h
Average speed of the van : Average speed of the sports car = 5 : 6
5 u + 6 u = 11 u
11 u = 165
1 u = 165 ÷ 11 = 15
Average speed of the sports car
= 6 u
= 6 x 15
= 90 km/h
(b)
Time taken for the van and the sports car to meet travelling the rest of the journey
= 165 ÷ 165
= 1 h
Answer(s): (a) 90 km/h; (b) 1 h