City P and City Q were 546 km apart. A car travelled from City P towards City Q. At the same time, a bus started from City Q to City P. After travelling 1¹₃ h, the two vehicles were still 378 km apart. If the ratio of the average speed of the bus to that of the car was 4 : 5, find

1. the average speed of the bus.
2. the time taken for them to meet travelling the rest of the journey. Express your answer in h.

(a)
Distance covered in 1¹₃ h by the two vehicles
= 546 - 378
= 168 km

Combined speed of the two vehicles
= 168 ÷ ⁴₃
= 168 x ³₄
= 126 km/h

Average speed of the bus : Average speed of the car = 4 : 5

4 u + 5 u = 9 u 
9 u = 126

1 u = 126 ÷ 9 = 14

Average speed of the bus
= 4 u
= 4 x 14
= 56 km/h

(b)
Time taken for the bus and the car to meet travelling the rest of the journey
= 378 ÷ 126
= 3 h 

Answer(s): (a) 56 km/h; (b) 3 h