City X and City Y were 539 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
12 h, the two vehicles were still 308 km apart. If the ratio of the average speed of the bus to that of the sedan was 5 : 6, 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
12 h by the two vehicles
= 539 - 308
= 231 km
Combined speed of the two vehicles
= 231 ÷
32 = 231 x
23 = 154 km/h
Average speed of the bus : Average speed of the sedan = 5 : 6
5 u + 6 u = 11 u
11 u = 154
1 u = 154 ÷ 11 = 14
Average speed of the sedan
= 6 u
= 6 x 14
= 84 km/h
(b)
Time taken for the bus and the sedan to meet travelling the rest of the journey
= 308 ÷ 154
= 2 h
Answer(s): (a) 84 km/h; (b) 2 h