City D and City E were 585 km apart. A car travelled from City D towards City E. At the same time, a van started from City E to City D. After travelling 1¹₃ h, the two vehicles were still 405 km apart. If the ratio of the average speed of the van to that of the car was 4 : 5, find

1. the average speed of the car.
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
= 585 - 405
= 180 km

Combined speed of the two vehicles
= 180 ÷ ⁴₃
= 180 x ³₄
= 135 km/h

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

4 u + 5 u = 9 u 
9 u = 135

1 u = 135 ÷ 9 = 15

Average speed of the car
= 5 u
= 5 x 15
= 75 km/h

(b)
Time taken for the van and the car to meet travelling the rest of the journey
= 405 ÷ 135
= 3 h 

Answer(s): (a) 75 km/h; (b) 3 h