City K and City L is 576 km apart. Jack left City K for City L at 10.00 a.m. travelling at an average speed of 72 km/h. Charlie left City K later than Jack and caught up with him at 2.00 p.m. Charlie was travelling at a speed of 108 km/h.

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

(a)
From 10.00 a.m. to 2.00 p.m. = 4 h

Distance that Jack covered when Charlie caught up with Jack
= 4 x 72
= 288 km

Time that Charlie took to travel 288 km
= 288 ÷ 108
= 2²₃ h

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

Time that Charlie left City K:
2 h 40 min before 2.00 p.m. = 11.20 a.m.

(b)
Remaining distance that they had to cover to reach City L
= 576 - 288
= 288 km

Duration that Charlie had to travel before reaching City L
= 288 ÷ 108
= 2²₃ h

Duration that Jack had to travel before reaching City L
= 288 ÷ 72
= 4 h

Duration that Jack took to arrive later than Charlie in City L
= 4 - 2²₃
= 1¹₃ h

Answer(s): (a) 11.20 a.m.; (b) 1¹₃ h