City V and City W is 480 km apart. Riordan left City V for City W at 10.00 a.m. travelling at an average speed of 60 km/h. Sam left City V later than Riordan and caught up with him at 1.00 p.m. Sam was travelling at a speed of 108 km/h.

1. At what time did Sam leave City V?
2. How much later did Riordan arrive in City W than Sam? Express your answer in h as a fraction or mixed number.

(a)
From 10.00 a.m. to 1.00 p.m. = 3 h

Distance that Riordan covered when Sam caught up with Riordan
= 3 x 60
= 180 km

Time that Sam 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 Sam left City V:
1 h 40 min before 1.00 p.m. = 11.20 a.m.

(b)
Remaining distance that they had to cover to reach City W
= 480 - 180
= 300 km

Duration that Sam had to travel before reaching City W
= 300 ÷ 108
= 2⁷₉ h

Duration that Riordan had to travel before reaching City W
= 300 ÷ 60
= 5 h

Duration that Riordan took to arrive later than Sam in City W
= 5 - 2⁷₉
= 2²₉ h

Answer(s): (a) 11.20 a.m.; (b) 2²₉ h