City T and City U were 567 km apart. A sports car travelled from City T towards City U. At the same time, a lorry started from City U to City T. After travelling 1¹₂ h, the two vehicles were still 378 km apart. If the ratio of the average speed of the lorry to that of the sports car was 4 : 5, find

1. the average speed of the sports car.
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
= 567 - 378
= 189 km

Combined speed of the two vehicles
= 189 ÷ ³₂
= 189 x ²₃
= 126 km/h

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

4 u + 5 u = 9 u 
9 u = 126

1 u = 126 ÷ 9 = 14

Average speed of the sports car
= 5 u
= 5 x 14
= 70 km/h

(b)
Time taken for the lorry and the sports car to meet travelling the rest of the journey
= 378 ÷ 126
= 3 h 

Answer(s): (a) 70 km/h; (b) 3 h