City G and City H is 330 km apart. Ryan left City G for City H at 10.00 a.m. travelling at an average speed of 66 km/h. Sam left City G later than Ryan 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 G?
2. How much later did Ryan arrive in City H 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 Ryan covered when Sam caught up with Ryan
= 3 x 66
= 198 km

Time that Sam took to travel 198 km
= 198 ÷ 108
= 1⁵₆ h

1 h = 60 min
⁵₆ h = ⁵₆ x 60 = 50 min
1⁵₆ h = 1 h 50 min

Time that Sam left City G:
1 h 50 min before 1.00 p.m. = 11.10 a.m.

(b)
Remaining distance that they had to cover to reach City H
= 330 - 198
= 132 km

Duration that Sam had to travel before reaching City H
= 132 ÷ 108
= 1²₉ h

Duration that Ryan had to travel before reaching City H
= 132 ÷ 66
= 2 h

Duration that Ryan took to arrive later than Sam in City H
= 2 - 1²₉
= ⁷₉ h

Answer(s): (a) 11.10 a.m.; (b) ⁷₉ h