City V and City W is 532 km apart. Ethan left City V for City W at 11.00 a.m. travelling at an average speed of 76 km/h. Valen left City V later than Ethan and caught up with him at 3.00 p.m. Valen was travelling at a speed of 114 km/h.

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

(a)
From 11.00 a.m. to 3.00 p.m. = 4 h

Distance that Ethan covered when Valen caught up with Ethan
= 4 x 76
= 304 km

Time that Valen took to travel 304 km
= 304 ÷ 114
= 2²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
2²₃ h = 2 h 40 min

Time that Valen left City V:
2 h 40 min before 3.00 p.m. = 12.20 p.m.

(b)
Remaining distance that they had to cover to reach City W
= 532 - 304
= 228 km

Duration that Valen had to travel before reaching City W
= 228 ÷ 114
= 2 h

Duration that Ethan had to travel before reaching City W
= 228 ÷ 76
= 3 h

Duration that Ethan took to arrive later than Valen in City W
= 3 - 2
= 1 h

Answer(s): (a) 12.20 p.m.; (b) 1 h