City K and City L is 320 km apart. Gabriel left City K for City L at 8.00 a.m. travelling at an average speed of 64 km/h. Liam left City K later than Gabriel and caught up with him at 11.00 a.m. Liam was travelling at a speed of 72 km/h.

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

(a)
From 8.00 a.m. to 11.00 a.m. = 3 h

Distance that Gabriel covered when Liam caught up with Gabriel
= 3 x 64
= 192 km

Time that Liam took to travel 192 km
= 192 ÷ 72
= 2²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
2²₃ h = 2 h 40 min

Time that Liam left City K:
2 h 40 min before 11.00 a.m. = 8.20 a.m.

(b)
Remaining distance that they had to cover to reach City L
= 320 - 192
= 128 km

Duration that Liam had to travel before reaching City L
= 128 ÷ 72
= 1⁷₉ h

Duration that Gabriel had to travel before reaching City L
= 128 ÷ 64
= 2 h

Duration that Gabriel took to arrive later than Liam in City L
= 2 - 1⁷₉
= ²₉ h

Answer(s): (a) 8.20 a.m.; (b) ²₉ h