City T and City U is 468 km apart. Will left City T for City U at 11.00 a.m. travelling at an average speed of 78 km/h. Mark left City T later than Will and caught up with him at 3.00 p.m. Mark was travelling at a speed of 117 km/h.

1. At what time did Mark leave City T?
2. How much later did Will arrive in City U than Mark? Express your answer in h as a fraction or mixed number.

(a)
From 11.00 a.m. to 3.00 p.m. = 4 h

Distance that Will covered when Mark caught up with Will
= 4 x 78
= 312 km

Time that Mark took to travel 312 km
= 312 ÷ 117
= 2²₃ h

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

Time that Mark left City T:
2 h 40 min before 3.00 p.m. = 12.20 p.m.

(b)
Remaining distance that they had to cover to reach City U
= 468 - 312
= 156 km

Duration that Mark had to travel before reaching City U
= 156 ÷ 117
= 1¹₃ h

Duration that Will had to travel before reaching City U
= 156 ÷ 78
= 2 h

Duration that Will took to arrive later than Mark in City U
= 2 - 1¹₃
= ²₃ h

Answer(s): (a) 12.20 p.m.; (b) ²₃ h