City A and City B is 264 km apart. Paul left City A for City B at 8.00 a.m. travelling at an average speed of 66 km/h. Liam left City A later than Paul and caught up with him at 10.00 a.m. Liam was travelling at a speed of 99 km/h.

1. At what time did Liam leave City A?
2. How much later did Paul arrive in City B than Liam? Express your answer in h as a fraction or mixed number.

(a)
From 8.00 a.m. to 10.00 a.m. = 2 h

Distance that Paul covered when Liam caught up with Paul
= 2 x 66
= 132 km

Time that Liam took to travel 132 km
= 132 ÷ 99
= 1¹₃ h

1 h = 60 min
¹₃ h = ¹₃ x 60 = 20 min
1¹₃ h = 1 h 20 min

Time that Liam left City A:
1 h 20 min before 10.00 a.m. = 8.40 a.m.

(b)
Remaining distance that they had to cover to reach City B
= 264 - 132
= 132 km

Duration that Liam had to travel before reaching City B
= 132 ÷ 99
= 1¹₃ h

Duration that Paul had to travel before reaching City B
= 132 ÷ 66
= 2 h

Duration that Paul took to arrive later than Liam in City B
= 2 - 1¹₃
= ²₃ h

Answer(s): (a) 8.40 a.m.; (b) ²₃ h