City Y and City Z is 594 km apart. Ben left City Y for City Z at 10.00 a.m. travelling at an average speed of 66 km/h. Liam left City Y later than Ben and caught up with him at 2.00 p.m. Liam was travelling at a speed of 96 km/h.

1. At what time did Liam leave City Y?
2. How much later did Ben arrive in City Z than Liam? 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 Ben covered when Liam caught up with Ben
= 4 x 66
= 264 km

Time that Liam took to travel 264 km
= 264 ÷ 96
= 2³₄ h

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

Time that Liam left City Y:
2 h 45 min before 2.00 p.m. = 11.15 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 594 - 264
= 330 km

Duration that Liam had to travel before reaching City Z
= 330 ÷ 96
= 3⁷₁₆ h

Duration that Ben had to travel before reaching City Z
= 330 ÷ 66
= 5 h

Duration that Ben took to arrive later than Liam in City Z
= 5 - 3⁷₁₆
= 1⁹₁₆ h

Answer(s): (a) 11.15 a.m.; (b) 1⁹₁₆ h