City W and City X is 504 km apart. Ben left City W for City X at 9.00 a.m. travelling at an average speed of 72 km/h. Justin left City W later than Ben and caught up with him at 12.00 p.m. Justin was travelling at a speed of 81 km/h.

1. At what time did Justin leave City W?
2. How much later did Ben arrive in City X than Justin? 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 Ben covered when Justin caught up with Ben
= 3 x 72
= 216 km

Time that Justin took to travel 216 km
= 216 ÷ 81
= 2²₃ h

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

Time that Justin left City W:
2 h 40 min before 12.00 p.m. = 9.20 a.m.

(b)
Remaining distance that they had to cover to reach City X
= 504 - 216
= 288 km

Duration that Justin had to travel before reaching City X
= 288 ÷ 81
= 3⁵₉ h

Duration that Ben had to travel before reaching City X
= 288 ÷ 72
= 4 h

Duration that Ben took to arrive later than Justin in City X
= 4 - 3⁵₉
= ⁴₉ h

Answer(s): (a) 9.20 a.m.; (b) ⁴₉ h