City K and City L is 252 km apart. Daniel left City K for City L at 7.00 a.m. travelling at an average speed of 63 km/h. Sam left City K later than Daniel and caught up with him at 9.00 a.m. Sam was travelling at a speed of 84 km/h.

1. At what time did Sam leave City K?
2. How much later did Daniel arrive in City L 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 ÷ 84
= 1¹₂ h

1 h = 60 min
¹₂ h = ¹₂ x 60 = 30 min
1¹₂ h = 1 h 30 min

Time that Sam left City K:
1 h 30 min before 9.00 a.m. = 7.30 a.m.

(b)
Remaining distance that they had to cover to reach City L
= 252 - 126
= 126 km

Duration that Sam had to travel before reaching City L
= 126 ÷ 84
= 1¹₂ h

Duration that Daniel had to travel before reaching City L
= 126 ÷ 63
= 2 h

Duration that Daniel took to arrive later than Sam in City L
= 2 - 1¹₂
= ¹₂ h

Answer(s): (a) 7.30 a.m.; (b) ¹₂ h