City J and City K were 585 km apart. A sedan travelled from City J towards City K. At the same time, a van started from City K to City J. After travelling 1
13 h, the two vehicles were still 405 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 sedan.
- the time taken for them to meet travelling the rest of the journey. Express your answer in h.
(a)
Distance covered in 1
13 h by the two vehicles
= 585 - 405
= 180 km
Combined speed of the two vehicles
= 180 ÷
43 = 180 x
34 = 135 km/h
Average speed of the van : Average speed of the sedan = 4 : 5
4 u + 5 u = 9 u
9 u = 135
1 u = 135 ÷ 9 = 15
Average speed of the sedan
= 5 u
= 5 x 15
= 75 km/h
(b)
Time taken for the van and the sedan to meet travelling the rest of the journey
= 405 ÷ 135
= 3 h
Answer(s): (a) 75 km/h; (b) 3 h