City J and City K is 330 km apart. Julian left City J for City K at 10.00 a.m. travelling at an average speed of 66 km/h. Ethan left City J later than Julian and caught up with him at 12.00 p.m. Ethan was travelling at a speed of 72 km/h.

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

(a)
From 10.00 a.m. to 12.00 p.m. = 2 h

Distance that Julian covered when Ethan caught up with Julian
= 2 x 66
= 132 km

Time that Ethan took to travel 132 km
= 132 ÷ 72
= 1⁵₆ h

1 h = 60 min
⁵₆ h = ⁵₆ x 60 = 50 min
1⁵₆ h = 1 h 50 min

Time that Ethan left City J:
1 h 50 min before 12.00 p.m. = 10.10 a.m.

(b)
Remaining distance that they had to cover to reach City K
= 330 - 132
= 198 km

Duration that Ethan had to travel before reaching City K
= 198 ÷ 72
= 2³₄ h

Duration that Julian had to travel before reaching City K
= 198 ÷ 66
= 3 h

Duration that Julian took to arrive later than Ethan in City K
= 3 - 2³₄
= ¹₄ h

Answer(s): (a) 10.10 a.m.; (b) ¹₄ h