City S and City T were 567 km apart. A car travelled from City S towards City T. At the same time, a lorry started from City T to City S. After travelling 1
15 h, the two vehicles were still 405 km apart. If the ratio of the average speed of the lorry to that of the car was 4 : 5, 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
15 h by the two vehicles
= 567 - 405
= 162 km
Combined speed of the two vehicles
= 162 ÷
65 = 162 x
56 = 135 km/h
Average speed of the lorry : Average speed of the car = 4 : 5
4 u + 5 u = 9 u
9 u = 135
1 u = 135 ÷ 9 = 15
Average speed of the car
= 5 u
= 5 x 15
= 75 km/h
(b)
Time taken for the lorry and the car to meet travelling the rest of the journey
= 405 ÷ 135
= 3 h
Answer(s): (a) 75 km/h; (b) 3 h