City Y and City Z is 520 km apart. Bobby left City Y for City Z at 11.00 a.m. travelling at an average speed of 65 km/h. Ahmad left City Y later than Bobby and caught up with him at 2.00 p.m. Ahmad was travelling at a speed of 90 km/h.

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

(a)
From 11.00 a.m. to 2.00 p.m. = 3 h

Distance that Bobby covered when Ahmad caught up with Bobby
= 3 x 65
= 195 km

Time that Ahmad took to travel 195 km
= 195 ÷ 90
= 2¹₆ h

1 h = 60 min
¹₆ h = ¹₆ x 60 = 10 min
2¹₆ h = 2 h 10 min

Time that Ahmad left City Y:
2 h 10 min before 2.00 p.m. = 11.50 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 520 - 195
= 325 km

Duration that Ahmad had to travel before reaching City Z
= 325 ÷ 90
= 3¹¹₁₈ h

Duration that Bobby had to travel before reaching City Z
= 325 ÷ 65
= 5 h

Duration that Bobby took to arrive later than Ahmad in City Z
= 5 - 3¹¹₁₈
= 1⁷₁₈ h

Answer(s): (a) 11.50 a.m.; (b) 1⁷₁₈ h