City X and City Y were 728 km apart. A van travelled from City X towards City Y. At the same time, a lorry started from City Y to City X. After travelling 1
12 h, the two vehicles were still 416 km apart. If the ratio of the average speed of the lorry to that of the van was 6 : 7, 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
12 h by the two vehicles
= 728 - 416
= 312 km
Combined speed of the two vehicles
= 312 ÷
32 = 312 x
23 = 208 km/h
Average speed of the lorry : Average speed of the van = 6 : 7
6 u + 7 u = 13 u
13 u = 208
1 u = 208 ÷ 13 = 16
Average speed of the lorry
= 6 u
= 6 x 16
= 96 km/h
(b)
Time taken for the lorry and the van to meet travelling the rest of the journey
= 416 ÷ 208
= 2 h
Answer(s): (a) 96 km/h; (b) 2 h