City N and City P were 507 km apart. A van travelled from City N towards City P. At the same time, a lorry started from City P to City N. After travelling 1¹₄ h, the two vehicles were still 312 km apart. If the ratio of the average speed of the lorry to that of the van was 6 : 7, 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
= 507 - 312
= 195 km

Combined speed of the two vehicles
= 195 ÷ ⁵₄
= 195 x ⁴₅
= 156 km/h

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

6 u + 7 u = 13 u 
13 u = 156

1 u = 156 ÷ 13 = 12

Average speed of the lorry
= 6 u
= 6 x 12
= 72 km/h

(b)
Time taken for the lorry and the van to meet travelling the rest of the journey
= 312 ÷ 156
= 2 h 

Answer(s): (a) 72 km/h; (b) 2 h