City D and City E is 378 km apart. Ian left City D for City E at 8.00 a.m. travelling at an average speed of 63 km/h. Ahmad left City D later than Ian and caught up with him at 12.00 p.m. Ahmad was travelling at a speed of 112 km/h.

1. At what time did Ahmad leave City D?
2. How much later did Ian arrive in City E than Ahmad? Express your answer in h as a fraction or mixed number.

(a)
From 8.00 a.m. to 12.00 p.m. = 4 h

Distance that Ian covered when Ahmad caught up with Ian
= 4 x 63
= 252 km

Time that Ahmad took to travel 252 km
= 252 ÷ 112
= 2¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
2¹₄ h = 2 h 15 min

Time that Ahmad left City D:
2 h 15 min before 12.00 p.m. = 9.45 a.m.

(b)
Remaining distance that they had to cover to reach City E
= 378 - 252
= 126 km

Duration that Ahmad had to travel before reaching City E
= 126 ÷ 112
= 1¹₈ h

Duration that Ian had to travel before reaching City E
= 126 ÷ 63
= 2 h

Duration that Ian took to arrive later than Ahmad in City E
= 2 - 1¹₈
= ⁷₈ h

Answer(s): (a) 9.45 a.m.; (b) ⁷₈ h