City Q and City R were 273 km apart. A sports car travelled from City Q towards City R. At the same time, a van started from City R to City Q. After travelling 1¹₃ h, the two vehicles were still 117 km apart. If the ratio of the average speed of the van to that of the sports car was 4 : 5, 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 1¹₃ h by the two vehicles
= 273 - 117
= 156 km

Combined speed of the two vehicles
= 156 ÷ ⁴₃
= 156 x ³₄
= 117 km/h

Average speed of the van : Average speed of the sports car = 4 : 5

4 u + 5 u = 9 u 
9 u = 117

1 u = 117 ÷ 9 = 13

Average speed of the van
= 4 u
= 4 x 13
= 52 km/h

(b)
Time taken for the van and the sports car to meet travelling the rest of the journey
= 117 ÷ 117
= 1 h 

Answer(s): (a) 52 km/h; (b) 1 h