City B and City C were 726 km apart. A van travelled from City B towards City C. At the same time, a bus started from City C to City B. After travelling 1
25 h, the two vehicles were still 495 km apart. If the ratio of the average speed of the bus to that of the van was 5 : 6, find
- the average speed of the bus.
- the time taken for them to meet travelling the rest of the journey. Express your answer in h.
(a)
Distance covered in 1
25 h by the two vehicles
= 726 - 495
= 231 km
Combined speed of the two vehicles
= 231 ÷
75 = 231 x
57 = 165 km/h
Average speed of the bus : Average speed of the van = 5 : 6
5 u + 6 u = 11 u
11 u = 165
1 u = 165 ÷ 11 = 15
Average speed of the bus
= 5 u
= 5 x 15
= 75 km/h
(b)
Time taken for the bus and the van to meet travelling the rest of the journey
= 495 ÷ 165
= 3 h
Answer(s): (a) 75 km/h; (b) 3 h