City B and City C were 693 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 462 km apart. If the ratio of the average speed of the van to that of the sports car was 5 : 6, find
- the average speed of the sports car.
- 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
= 693 - 462
= 231 km
Combined speed of the two vehicles
= 231 ÷
32 = 231 x
23 = 154 km/h
Average speed of the van : Average speed of the sports car = 5 : 6
5 u + 6 u = 11 u
11 u = 154
1 u = 154 ÷ 11 = 14
Average speed of the sports car
= 6 u
= 6 x 14
= 84 km/h
(b)
Time taken for the van and the sports car to meet travelling the rest of the journey
= 462 ÷ 154
= 3 h
Answer(s): (a) 84 km/h; (b) 3 h