City J and City K is 325 km apart. Owen left City J for City K at 9.00 a.m. travelling at an average speed of 65 km/h. Tom left City J later than Owen and caught up with him at 12.00 p.m. Tom was travelling at a speed of 78 km/h.

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

(a)
From 9.00 a.m. to 12.00 p.m. = 3 h

Distance that Owen covered when Tom caught up with Owen
= 3 x 65
= 195 km

Time that Tom took to travel 195 km
= 195 ÷ 78
= 2¹₂ h

1 h = 60 min
¹₂ h = ¹₂ x 60 = 30 min
2¹₂ h = 2 h 30 min

Time that Tom left City J:
2 h 30 min before 12.00 p.m. = 9.30 a.m.

(b)
Remaining distance that they had to cover to reach City K
= 325 - 195
= 130 km

Duration that Tom had to travel before reaching City K
= 130 ÷ 78
= 1²₃ h

Duration that Owen had to travel before reaching City K
= 130 ÷ 65
= 2 h

Duration that Owen took to arrive later than Tom in City K
= 2 - 1²₃
= ¹₃ h

Answer(s): (a) 9.30 a.m.; (b) ¹₃ h