City S and City T were 459 km apart. A sedan travelled from City S towards City T. At the same time, a lorry started from City T to City S. After travelling 1¹₄ h, the two vehicles were still 324 km apart. If the ratio of the average speed of the lorry to that of the sedan was 4 : 5, find

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

(a)
Distance covered in 1¹₄ h by the two vehicles
= 459 - 324
= 135 km

Combined speed of the two vehicles
= 135 ÷ ⁵₄
= 135 x ⁴₅
= 108 km/h

Average speed of the lorry : Average speed of the sedan = 4 : 5

4 u + 5 u = 9 u 
9 u = 108

1 u = 108 ÷ 9 = 12

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

(b)
Time taken for the lorry and the sedan to meet travelling the rest of the journey
= 324 ÷ 108
= 3 h 

Answer(s): (a) 48 km/h; (b) 3 h