City K and City L is 252 km apart. Japheth left City K for City L at 7.00 a.m. travelling at an average speed of 63 km/h. Luis left City K later than Japheth and caught up with him at 9.00 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 Japheth arrive in City L than Luis? Express your answer in h as a fraction or mixed number.

(a)
From 7.00 a.m. to 9.00 a.m. = 2 h

Distance that Japheth covered when Luis caught up with Japheth
= 2 x 63
= 126 km

Time that Luis took to travel 126 km
= 126 ÷ 108
= 1¹₆ h

1 h = 60 min
¹₆ h = ¹₆ x 60 = 10 min
1¹₆ h = 1 h 10 min

Time that Luis left City K:
1 h 10 min before 9.00 a.m. = 7.50 a.m.

(b)
Remaining distance that they had to cover to reach City L
= 252 - 126
= 126 km

Duration that Luis had to travel before reaching City L
= 126 ÷ 108
= 1¹₆ h

Duration that Japheth had to travel before reaching City L
= 126 ÷ 63
= 2 h

Duration that Japheth took to arrive later than Luis in City L
= 2 - 1¹₆
= ⁵₆ h

Answer(s): (a) 7.50 a.m.; (b) ⁵₆ h