City K and City L is 420 km apart. Cody left City K for City L at 11.00 a.m. travelling at an average speed of 60 km/h. Ben left City K later than Cody and caught up with him at 2.00 p.m. Ben was travelling at a speed of 108 km/h.

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

(a)
From 11.00 a.m. to 2.00 p.m. = 3 h

Distance that Cody covered when Ben caught up with Cody
= 3 x 60
= 180 km

Time that Ben took to travel 180 km
= 180 ÷ 108
= 1²₃ h

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

Time that Ben left City K:
1 h 40 min before 2.00 p.m. = 12.20 p.m.

(b)
Remaining distance that they had to cover to reach City L
= 420 - 180
= 240 km

Duration that Ben had to travel before reaching City L
= 240 ÷ 108
= 2²₉ h

Duration that Cody had to travel before reaching City L
= 240 ÷ 60
= 4 h

Duration that Cody took to arrive later than Ben in City L
= 4 - 2²₉
= 1⁷₉ h

Answer(s): (a) 12.20 p.m.; (b) 1⁷₉ h