City K and City L is 325 km apart. Lee left City K for City L at 9.00 a.m. travelling at an average speed of 65 km/h. Ethan left City K later than Lee and caught up with him at 12.00 p.m. Ethan was travelling at a speed of 117 km/h.

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

(a)
From 9.00 a.m. to 12.00 p.m. = 3 h

Distance that Lee covered when Ethan caught up with Lee
= 3 x 65
= 195 km

Time that Ethan took to travel 195 km
= 195 ÷ 117
= 1²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
1²₃ h = 1 h 40 min

Time that Ethan left City K:
1 h 40 min before 12.00 p.m. = 10.20 a.m.

(b)
Remaining distance that they had to cover to reach City L
= 325 - 195
= 130 km

Duration that Ethan had to travel before reaching City L
= 130 ÷ 117
= 1¹₉ h

Duration that Lee had to travel before reaching City L
= 130 ÷ 65
= 2 h

Duration that Lee took to arrive later than Ethan in City L
= 2 - 1¹₉
= ⁸₉ h

Answer(s): (a) 10.20 a.m.; (b) ⁸₉ h