City L and City M were 429 km apart. A sports car travelled from City L towards City M. At the same time, a lorry started from City M to City L. After travelling 1
14 h, the two vehicles were still 264 km apart. If the ratio of the average speed of the lorry to that of the sports car was 5 : 6, find
- the average speed of the lorry.
- the time taken for them to meet travelling the rest of the journey. Express your answer in h.
(a)
Distance covered in 1
14 h by the two vehicles
= 429 - 264
= 165 km
Combined speed of the two vehicles
= 165 ÷
54 = 165 x
45 = 132 km/h
Average speed of the lorry : Average speed of the sports car = 5 : 6
5 u + 6 u = 11 u
11 u = 132
1 u = 132 ÷ 11 = 12
Average speed of the lorry
= 5 u
= 5 x 12
= 60 km/h
(b)
Time taken for the lorry and the sports car to meet travelling the rest of the journey
= 264 ÷ 132
= 2 h
Answer(s): (a) 60 km/h; (b) 2 h