City K and City L were 648 km apart. A van travelled from City K towards City L. At the same time, a bus started from City L to City K. After travelling 1
12 h, the two vehicles were still 432 km apart. If the ratio of the average speed of the bus 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
12 h by the two vehicles
= 648 - 432
= 216 km
Combined speed of the two vehicles
= 216 ÷
32 = 216 x
23 = 144 km/h
Average speed of the bus : Average speed of the van = 4 : 5
4 u + 5 u = 9 u
9 u = 144
1 u = 144 ÷ 9 = 16
Average speed of the van
= 5 u
= 5 x 16
= 80 km/h
(b)
Time taken for the bus and the van to meet travelling the rest of the journey
= 432 ÷ 144
= 3 h
Answer(s): (a) 80 km/h; (b) 3 h