City F and City G is 624 km apart. Luke left City F for City G at 9.00 a.m. travelling at an average speed of 78 km/h. Sean left City F later than Luke and caught up with him at 12.00 p.m. Sean was travelling at a speed of 104 km/h.

1. At what time did Sean leave City F?
2. How much later did Luke arrive in City G than Sean? 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 Luke covered when Sean caught up with Luke
= 3 x 78
= 234 km

Time that Sean took to travel 234 km
= 234 ÷ 104
= 2¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
2¹₄ h = 2 h 15 min

Time that Sean left City F:
2 h 15 min before 12.00 p.m. = 9.45 a.m.

(b)
Remaining distance that they had to cover to reach City G
= 624 - 234
= 390 km

Duration that Sean had to travel before reaching City G
= 390 ÷ 104
= 3³₄ h

Duration that Luke had to travel before reaching City G
= 390 ÷ 78
= 5 h

Duration that Luke took to arrive later than Sean in City G
= 5 - 3³₄
= 1¹₄ h

Answer(s): (a) 9.45 a.m.; (b) 1¹₄ h