City X and City Y is 616 km apart. Valen left City X for City Y at 11.00 a.m. travelling at an average speed of 77 km/h. Carl left City X later than Valen and caught up with him at 2.00 p.m. Carl was travelling at a speed of 84 km/h.

1. At what time did Carl leave City X?
2. How much later did Valen arrive in City Y than Carl? 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 Valen covered when Carl caught up with Valen
= 3 x 77
= 231 km

Time that Carl took to travel 231 km
= 231 ÷ 84
= 2³₄ h

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

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

(b)
Remaining distance that they had to cover to reach City Y
= 616 - 231
= 385 km

Duration that Carl had to travel before reaching City Y
= 385 ÷ 84
= 4⁷₁₂ h

Duration that Valen had to travel before reaching City Y
= 385 ÷ 77
= 5 h

Duration that Valen took to arrive later than Carl in City Y
= 5 - 4⁷₁₂
= ⁵₁₂ h

Answer(s): (a) 11.15 a.m.; (b) ⁵₁₂ h