City P and City Q were 588 km apart. A sedan travelled from City P towards City Q. At the same time, a van started from City Q to City P. After travelling 1
23 h, the two vehicles were still 378 km apart. If the ratio of the average speed of the van to that of the sedan 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
23 h by the two vehicles
= 588 - 378
= 210 km
Combined speed of the two vehicles
= 210 ÷
53 = 210 x
35 = 126 km/h
Average speed of the van : Average speed of the sedan = 4 : 5
4 u + 5 u = 9 u
9 u = 126
1 u = 126 ÷ 9 = 14
Average speed of the van
= 4 u
= 4 x 14
= 56 km/h
(b)
Time taken for the van and the sedan to meet travelling the rest of the journey
= 378 ÷ 126
= 3 h
Answer(s): (a) 56 km/h; (b) 3 h