City J and City K is 612 km apart. Bobby left City J for City K at 9.00 a.m. travelling at an average speed of 68 km/h. Julian left City J later than Bobby and caught up with him at 1.00 p.m. Julian was travelling at a speed of 102 km/h.

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

(a)
From 9.00 a.m. to 1.00 p.m. = 4 h

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

Time that Julian 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 Julian left City J:
2 h 40 min before 1.00 p.m. = 10.20 a.m.

(b)
Remaining distance that they had to cover to reach City K
= 612 - 272
= 340 km

Duration that Julian had to travel before reaching City K
= 340 ÷ 102
= 3¹₃ h

Duration that Bobby had to travel before reaching City K
= 340 ÷ 68
= 5 h

Duration that Bobby took to arrive later than Julian in City K
= 5 - 3¹₃
= 1²₃ h

Answer(s): (a) 10.20 a.m.; (b) 1²₃ h