City F and City G is 408 km apart. Bobby left City F for City G at 11.00 a.m. travelling at an average speed of 68 km/h. Michael left City F later than Bobby and caught up with him at 3.00 p.m. Michael was travelling at a speed of 102 km/h.

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

(a)
From 11.00 a.m. to 3.00 p.m. = 4 h

Distance that Bobby covered when Michael caught up with Bobby
= 4 x 68
= 272 km

Time that Michael took to travel 272 km
= 272 ÷ 102
= 2²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
2²₃ h = 2 h 40 min

Time that Michael left City F:
2 h 40 min before 3.00 p.m. = 12.20 p.m.

(b)
Remaining distance that they had to cover to reach City G
= 408 - 272
= 136 km

Duration that Michael had to travel before reaching City G
= 136 ÷ 102
= 1¹₃ h

Duration that Bobby had to travel before reaching City G
= 136 ÷ 68
= 2 h

Duration that Bobby took to arrive later than Michael in City G
= 2 - 1¹₃
= ²₃ h

Answer(s): (a) 12.20 p.m.; (b) ²₃ h