City M and City N is 396 km apart. Liam left City M for City N at 7.00 a.m. travelling at an average speed of 66 km/h. Ivan left City M later than Liam and caught up with him at 10.00 a.m. Ivan was travelling at a speed of 72 km/h.

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

(a)
From 7.00 a.m. to 10.00 a.m. = 3 h

Distance that Liam covered when Ivan caught up with Liam
= 3 x 66
= 198 km

Time that Ivan took to travel 198 km
= 198 ÷ 72
= 2³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
2³₄ h = 2 h 45 min

Time that Ivan left City M:
2 h 45 min before 10.00 a.m. = 7.15 a.m.

(b)
Remaining distance that they had to cover to reach City N
= 396 - 198
= 198 km

Duration that Ivan had to travel before reaching City N
= 198 ÷ 72
= 2³₄ h

Duration that Liam had to travel before reaching City N
= 198 ÷ 66
= 3 h

Duration that Liam took to arrive later than Ivan in City N
= 3 - 2³₄
= ¹₄ h

Answer(s): (a) 7.15 a.m.; (b) ¹₄ h