City T and City U were 495 km apart. A van travelled from City T towards City U. At the same time, a lorry started from City U to City T. After travelling 1
23 h, the two vehicles were still 270 km apart. If the ratio of the average speed of the lorry to that of the van was 4 : 5, find
- the average speed of the van.
- 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
= 495 - 270
= 225 km
Combined speed of the two vehicles
= 225 ÷
53 = 225 x
35 = 135 km/h
Average speed of the lorry : Average speed of the van = 4 : 5
4 u + 5 u = 9 u
9 u = 135
1 u = 135 ÷ 9 = 15
Average speed of the van
= 5 u
= 5 x 15
= 75 km/h
(b)
Time taken for the lorry and the van to meet travelling the rest of the journey
= 270 ÷ 135
= 2 h
Answer(s): (a) 75 km/h; (b) 2 h