City E and City F is 414 km apart. David left City E for City F at 7.00 a.m. travelling at an average speed of 69 km/h. Luke left City E later than David and caught up with him at 10.00 a.m. Luke was travelling at a speed of 92 km/h.

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

(a)
From 7.00 a.m. to 10.00 a.m. = 3 h

Distance that David covered when Luke caught up with David
= 3 x 69
= 207 km

Time that Luke took to travel 207 km
= 207 ÷ 92
= 2¹₄ h

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

Time that Luke left City E:
2 h 15 min before 10.00 a.m. = 7.45 a.m.

(b)
Remaining distance that they had to cover to reach City F
= 414 - 207
= 207 km

Duration that Luke had to travel before reaching City F
= 207 ÷ 92
= 2¹₄ h

Duration that David had to travel before reaching City F
= 207 ÷ 69
= 3 h

Duration that David took to arrive later than Luke in City F
= 3 - 2¹₄
= ³₄ h

Answer(s): (a) 7.45 a.m.; (b) ³₄ h