City W and City X were 819 km apart. A sedan travelled from City W towards City X. At the same time, a van started from City X to City W. After travelling 1¹₅ h, the two vehicles were still 585 km apart. If the ratio of the average speed of the van to that of the sedan was 6 : 7, 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 1¹₅ h by the two vehicles
= 819 - 585
= 234 km

Combined speed of the two vehicles
= 234 ÷ ⁶₅
= 234 x ⁵₆
= 195 km/h

Average speed of the van : Average speed of the sedan = 6 : 7

6 u + 7 u = 13 u 
13 u = 195

1 u = 195 ÷ 13 = 15

Average speed of the van
= 6 u
= 6 x 15
= 90 km/h

(b)
Time taken for the van and the sedan to meet travelling the rest of the journey
= 585 ÷ 195
= 3 h 

Answer(s): (a) 90 km/h; (b) 3 h