City K and City L is 420 km apart. Xavier left City K for City L at 8.00 a.m. travelling at an average speed of 60 km/h. Justin left City K later than Xavier and caught up with him at 10.00 a.m. Justin was travelling at a speed of 80 km/h.

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

(a)
From 8.00 a.m. to 10.00 a.m. = 2 h

Distance that Xavier covered when Justin caught up with Xavier
= 2 x 60
= 120 km

Time that Justin took to travel 120 km
= 120 ÷ 80
= 1¹₂ h

1 h = 60 min
¹₂ h = ¹₂ x 60 = 30 min
1¹₂ h = 1 h 30 min

Time that Justin left City K:
1 h 30 min before 10.00 a.m. = 8.30 a.m.

(b)
Remaining distance that they had to cover to reach City L
= 420 - 120
= 300 km

Duration that Justin had to travel before reaching City L
= 300 ÷ 80
= 3³₄ h

Duration that Xavier had to travel before reaching City L
= 300 ÷ 60
= 5 h

Duration that Xavier took to arrive later than Justin in City L
= 5 - 3³₄
= 1¹₄ h

Answer(s): (a) 8.30 a.m.; (b) 1¹₄ h