City L and City M were 612 km apart. A van travelled from City L towards City M. At the same time, a bus started from City M to City L. After travelling 1¹₄ h, the two vehicles were still 432 km apart. If the ratio of the average speed of the bus to that of the van 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 1¹₄ h by the two vehicles
= 612 - 432
= 180 km

Combined speed of the two vehicles
= 180 ÷ ⁵₄
= 180 x ⁴₅
= 144 km/h

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

4 u + 5 u = 9 u 
9 u = 144

1 u = 144 ÷ 9 = 16

Average speed of the bus
= 4 u
= 4 x 16
= 64 km/h

(b)
Time taken for the bus and the van to meet travelling the rest of the journey
= 432 ÷ 144
= 3 h 

Answer(s): (a) 64 km/h; (b) 3 h