City D and City E were 780 km apart. A sports car travelled from City D towards City E. At the same time, a van started from City E to City D. After travelling 1
34 h, the two vehicles were still 416 km apart. If the ratio of the average speed of the van to that of the sports car was 6 : 7, 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
34 h by the two vehicles
= 780 - 416
= 364 km
Combined speed of the two vehicles
= 364 ÷
74 = 364 x
47 = 208 km/h
Average speed of the van : Average speed of the sports car = 6 : 7
6 u + 7 u = 13 u
13 u = 208
1 u = 208 ÷ 13 = 16
Average speed of the van
= 6 u
= 6 x 16
= 96 km/h
(b)
Time taken for the van and the sports car to meet travelling the rest of the journey
= 416 ÷ 208
= 2 h
Answer(s): (a) 96 km/h; (b) 2 h