City B and City C were 363 km apart. A sports car travelled from City B towards City C. At the same time, a bus started from City C to City B. After travelling 1³₄ h, the two vehicles were still 132 km apart. If the ratio of the average speed of the bus to that of the sports car was 5 : 6, 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
= 363 - 132
= 231 km

Combined speed of the two vehicles
= 231 ÷ ⁷₄
= 231 x ⁴₇
= 132 km/h

Average speed of the bus : Average speed of the sports car = 5 : 6

5 u + 6 u = 11 u 
11 u = 132

1 u = 132 ÷ 11 = 12

Average speed of the bus
= 5 u
= 5 x 12
= 60 km/h

(b)
Time taken for the bus and the sports car to meet travelling the rest of the journey
= 132 ÷ 132
= 1 h 

Answer(s): (a) 60 km/h; (b) 1 h