City P and City Q were 780 km apart. A sedan travelled from City P towards City Q. At the same time, a bus started from City Q to City P. After travelling 1³₄ h, the two vehicles were still 416 km apart. If the ratio of the average speed of the bus to that of the sedan was 6 : 7, find

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

(a)
Distance covered in 1³₄ h by the two vehicles
= 780 - 416
= 364 km

Combined speed of the two vehicles
= 364 ÷ ⁷₄
= 364 x ⁴₇
= 208 km/h

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

6 u + 7 u = 13 u 
13 u = 208

1 u = 208 ÷ 13 = 16

Average speed of the bus
= 6 u
= 6 x 16
= 96 km/h

(b)
Time taken for the bus and the sedan to meet travelling the rest of the journey
= 416 ÷ 208
= 2 h 

Answer(s): (a) 96 km/h; (b) 2 h