City T and City U is 528 km apart. Rael left City T for City U at 11.00 a.m. travelling at an average speed of 66 km/h. Luke left City T later than Rael and caught up with him at 2.00 p.m. Luke was travelling at a speed of 88 km/h.

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

(a)
From 11.00 a.m. to 2.00 p.m. = 3 h

Distance that Rael covered when Luke caught up with Rael
= 3 x 66
= 198 km

Time that Luke took to travel 198 km
= 198 ÷ 88
= 2¹₄ h

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

Time that Luke left City T:
2 h 15 min before 2.00 p.m. = 11.45 a.m.

(b)
Remaining distance that they had to cover to reach City U
= 528 - 198
= 330 km

Duration that Luke had to travel before reaching City U
= 330 ÷ 88
= 3³₄ h

Duration that Rael had to travel before reaching City U
= 330 ÷ 66
= 5 h

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

Answer(s): (a) 11.45 a.m.; (b) 1¹₄ h