City E and City F were 663 km apart. A sports car travelled from City E towards City F. At the same time, a lorry started from City F to City E. After travelling 1
25 h, the two vehicles were still 390 km apart. If the ratio of the average speed of the lorry 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
25 h by the two vehicles
= 663 - 390
= 273 km
Combined speed of the two vehicles
= 273 ÷
75 = 273 x
57 = 195 km/h
Average speed of the lorry : 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 lorry and the sports car to meet travelling the rest of the journey
= 390 ÷ 195
= 2 h
Answer(s): (a) 105 km/h; (b) 2 h