City K and City L is 396 km apart. Ethan left City K for City L at 7.00 a.m. travelling at an average speed of 66 km/h. Luis left City K later than Ethan and caught up with him at 10.00 a.m. Luis was travelling at a speed of 108 km/h.

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

(a)
From 7.00 a.m. to 10.00 a.m. = 3 h

Distance that Ethan covered when Luis caught up with Ethan
= 3 x 66
= 198 km

Time that Luis took to travel 198 km
= 198 ÷ 108
= 1⁵₆ h

1 h = 60 min
⁵₆ h = ⁵₆ x 60 = 50 min
1⁵₆ h = 1 h 50 min

Time that Luis left City K:
1 h 50 min before 10.00 a.m. = 8.10 a.m.

(b)
Remaining distance that they had to cover to reach City L
= 396 - 198
= 198 km

Duration that Luis had to travel before reaching City L
= 198 ÷ 108
= 1⁵₆ h

Duration that Ethan had to travel before reaching City L
= 198 ÷ 66
= 3 h

Duration that Ethan took to arrive later than Luis in City L
= 3 - 1⁵₆
= 1¹₆ h

Answer(s): (a) 8.10 a.m.; (b) 1¹₆ h