City U and City V is 304 km apart. Carl left City U for City V at 9.00 a.m. travelling at an average speed of 76 km/h. Liam left City U later than Carl and caught up with him at 11.00 a.m. Liam was travelling at a speed of 96 km/h.

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

(a)
From 9.00 a.m. to 11.00 a.m. = 2 h

Distance that Carl covered when Liam caught up with Carl
= 2 x 76
= 152 km

Time that Liam took to travel 152 km
= 152 ÷ 96
= 1⁷₁₂ h

1 h = 60 min
⁷₁₂ h = ⁷₁₂ x 60 = 35 min
1⁷₁₂ h = 1 h 35 min

Time that Liam left City U:
1 h 35 min before 11.00 a.m. = 9.25 a.m.

(b)
Remaining distance that they had to cover to reach City V
= 304 - 152
= 152 km

Duration that Liam had to travel before reaching City V
= 152 ÷ 96
= 1⁷₁₂ h

Duration that Carl had to travel before reaching City V
= 152 ÷ 76
= 2 h

Duration that Carl took to arrive later than Liam in City V
= 2 - 1⁷₁₂
= ⁵₁₂ h

Answer(s): (a) 9.25 a.m.; (b) ⁵₁₂ h