City W and City X is 420 km apart. Charlie left City W for City X at 7.00 a.m. travelling at an average speed of 70 km/h. Ahmad left City W later than Charlie and caught up with him at 9.00 a.m. Ahmad was travelling at a speed of 84 km/h.

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

(a)
From 7.00 a.m. to 9.00 a.m. = 2 h

Distance that Charlie covered when Ahmad caught up with Charlie
= 2 x 70
= 140 km

Time that Ahmad took to travel 140 km
= 140 ÷ 84
= 1²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
1²₃ h = 1 h 40 min

Time that Ahmad left City W:
1 h 40 min before 9.00 a.m. = 7.20 a.m.

(b)
Remaining distance that they had to cover to reach City X
= 420 - 140
= 280 km

Duration that Ahmad had to travel before reaching City X
= 280 ÷ 84
= 3¹₃ h

Duration that Charlie had to travel before reaching City X
= 280 ÷ 70
= 4 h

Duration that Charlie took to arrive later than Ahmad in City X
= 4 - 3¹₃
= ²₃ h

Answer(s): (a) 7.20 a.m.; (b) ²₃ h