City S and City T is 378 km apart. Mark left City S for City T at 8.00 a.m. travelling at an average speed of 63 km/h. Michael left City S later than Mark and caught up with him at 10.00 a.m. Michael was travelling at a speed of 84 km/h.

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

(a)
From 8.00 a.m. to 10.00 a.m. = 2 h

Distance that Mark covered when Michael caught up with Mark
= 2 x 63
= 126 km

Time that Michael 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 Michael left City S:
1 h 30 min before 10.00 a.m. = 8.30 a.m.

(b)
Remaining distance that they had to cover to reach City T
= 378 - 126
= 252 km

Duration that Michael had to travel before reaching City T
= 252 ÷ 84
= 3 h

Duration that Mark had to travel before reaching City T
= 252 ÷ 63
= 4 h

Duration that Mark took to arrive later than Michael in City T
= 4 - 3
= 1 h

Answer(s): (a) 8.30 a.m.; (b) 1 h