City E and City F were 405 km apart. A van travelled from City E towards City F. At the same time, a bus started from City F to City E. After travelling 1³₄ h, the two vehicles were still 216 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 1³₄ h by the two vehicles
= 405 - 216
= 189 km

Combined speed of the two vehicles
= 189 ÷ ⁷₄
= 189 x ⁴₇
= 108 km/h

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

4 u + 5 u = 9 u 
9 u = 108

1 u = 108 ÷ 9 = 12

Average speed of the bus
= 4 u
= 4 x 12
= 48 km/h

(b)
Time taken for the bus and the van to meet travelling the rest of the journey
= 216 ÷ 108
= 2 h 

Answer(s): (a) 48 km/h; (b) 2 h