City L and City M is 462 km apart. Luis left City L for City M at 10.00 a.m. travelling at an average speed of 66 km/h. George left City L later than Luis and caught up with him at 2.00 p.m. George was travelling at a speed of 99 km/h.

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

(a)
From 10.00 a.m. to 2.00 p.m. = 4 h

Distance that Luis covered when George caught up with Luis
= 4 x 66
= 264 km

Time that George took to travel 264 km
= 264 ÷ 99
= 2²₃ h

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

Time that George left City L:
2 h 40 min before 2.00 p.m. = 11.20 a.m.

(b)
Remaining distance that they had to cover to reach City M
= 462 - 264
= 198 km

Duration that George had to travel before reaching City M
= 198 ÷ 99
= 2 h

Duration that Luis had to travel before reaching City M
= 198 ÷ 66
= 3 h

Duration that Luis took to arrive later than George in City M
= 3 - 2
= 1 h

Answer(s): (a) 11.20 a.m.; (b) 1 h