City B and City C were 378 km apart. A sports car travelled from City B towards City C. At the same time, a van started from City C to City B. After travelling 1
12 h, the two vehicles were still 216 km apart. If the ratio of the average speed of the van to that of the sports car 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
= 378 - 216
= 162 km
Combined speed of the two vehicles
= 162 ÷
32 = 162 x
23 = 108 km/h
Average speed of the van : Average speed of the sports car = 4 : 5
4 u + 5 u = 9 u
9 u = 108
1 u = 108 ÷ 9 = 12
Average speed of the van
= 4 u
= 4 x 12
= 48 km/h
(b)
Time taken for the van and the sports car to meet travelling the rest of the journey
= 216 ÷ 108
= 2 h
Answer(s): (a) 48 km/h; (b) 2 h