City Y and City Z were 546 km apart. A van travelled from City Y towards City Z. At the same time, a bus started from City Z to City Y. After travelling 1¹₂ h, the two vehicles were still 312 km apart. If the ratio of the average speed of the bus to that of the van was 6 : 7, find

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

(a)
Distance covered in 1¹₂ h by the two vehicles
= 546 - 312
= 234 km

Combined speed of the two vehicles
= 234 ÷ ³₂
= 234 x ²₃
= 156 km/h

Average speed of the bus : Average speed of the van = 6 : 7

6 u + 7 u = 13 u 
13 u = 156

1 u = 156 ÷ 13 = 12

Average speed of the van
= 7 u
= 7 x 12
= 84 km/h

(b)
Time taken for the bus and the van to meet travelling the rest of the journey
= 312 ÷ 156
= 2 h 

Answer(s): (a) 84 km/h; (b) 2 h