City B and City C were 572 km apart. A car travelled from City B towards City C. At the same time, a van started from City C to City B. After travelling 1²₃ h, the two vehicles were still 312 km apart. If the ratio of the average speed of the van to that of the car was 6 : 7, find

1. the average speed of the car.
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
= 572 - 312
= 260 km

Combined speed of the two vehicles
= 260 ÷ ⁵₃
= 260 x ³₅
= 156 km/h

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

6 u + 7 u = 13 u 
13 u = 156

1 u = 156 ÷ 13 = 12

Average speed of the car
= 7 u
= 7 x 12
= 84 km/h

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

Answer(s): (a) 84 km/h; (b) 2 h