City G and City H were 504 km apart. A sports car travelled from City G towards City H. At the same time, a van started from City H to City G. After travelling 1
23 h, the two vehicles were still 324 km apart. If the ratio of the average speed of the van to that of the sports car was 4 : 5, 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
23 h by the two vehicles
= 504 - 324
= 180 km
Combined speed of the two vehicles
= 180 ÷
53 = 180 x
35 = 108 km/h
Average speed of the van : Average speed of the sports car = 4 : 5
4 u + 5 u = 9 u
9 u = 108
1 u = 108 ÷ 9 = 12
Average speed of the sports car
= 5 u
= 5 x 12
= 60 km/h
(b)
Time taken for the van and the sports car to meet travelling the rest of the journey
= 324 ÷ 108
= 3 h
Answer(s): (a) 60 km/h; (b) 3 h