City J and City K is 315 km apart. Daniel left City J for City K at 7.00 a.m. travelling at an average speed of 63 km/h. Sam left City J later than Daniel and caught up with him at 9.00 a.m. Sam was travelling at a speed of 72 km/h.

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

(a)
From 7.00 a.m. to 9.00 a.m. = 2 h

Distance that Daniel covered when Sam caught up with Daniel
= 2 x 63
= 126 km

Time that Sam took to travel 126 km
= 126 ÷ 72
= 1³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
1³₄ h = 1 h 45 min

Time that Sam left City J:
1 h 45 min before 9.00 a.m. = 7.15 a.m.

(b)
Remaining distance that they had to cover to reach City K
= 315 - 126
= 189 km

Duration that Sam had to travel before reaching City K
= 189 ÷ 72
= 2⁵₈ h

Duration that Daniel had to travel before reaching City K
= 189 ÷ 63
= 3 h

Duration that Daniel took to arrive later than Sam in City K
= 3 - 2⁵₈
= ³₈ h

Answer(s): (a) 7.15 a.m.; (b) ³₈ h