City X and City Y were 546 km apart. A sedan travelled from City X towards City Y. At the same time, a bus started from City Y to City X. After travelling 1
23 h, the two vehicles were still 351 km apart. If the ratio of the average speed of the bus 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
23 h by the two vehicles
= 546 - 351
= 195 km
Combined speed of the two vehicles
= 195 ÷
53 = 195 x
35 = 117 km/h
Average speed of the bus : Average speed of the sedan = 4 : 5
4 u + 5 u = 9 u
9 u = 117
1 u = 117 ÷ 9 = 13
Average speed of the sedan
= 5 u
= 5 x 13
= 65 km/h
(b)
Time taken for the bus and the sedan to meet travelling the rest of the journey
= 351 ÷ 117
= 3 h
Answer(s): (a) 65 km/h; (b) 3 h