City H and City J were 360 km apart. A sedan travelled from City H towards City J. At the same time, a lorry started from City J to City H. After travelling 1²₃ h, the two vehicles were still 135 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 sedan.
2. the time taken for them to meet travelling the rest of the journey. Express your answer in h.

(a)
Distance covered in 1²₃ h by the two vehicles
= 360 - 135
= 225 km

Combined speed of the two vehicles
= 225 ÷ ⁵₃
= 225 x ³₅
= 135 km/h

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

4 u + 5 u = 9 u 
9 u = 135

1 u = 135 ÷ 9 = 15

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

(b)
Time taken for the lorry and the sedan to meet travelling the rest of the journey
= 135 ÷ 135
= 1 h 

Answer(s): (a) 75 km/h; (b) 1 h