City K and City L is 525 km apart. Brandon left City K for City L at 9.00 a.m. travelling at an average speed of 75 km/h. Luke left City K later than Brandon and caught up with him at 12.00 p.m. Luke was travelling at a speed of 100 km/h.

1. At what time did Luke leave City K?
2. How much later did Brandon arrive in City L than Luke? 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 Brandon covered when Luke caught up with Brandon
= 3 x 75
= 225 km

Time that Luke took to travel 225 km
= 225 ÷ 100
= 2¹₄ h

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

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

(b)
Remaining distance that they had to cover to reach City L
= 525 - 225
= 300 km

Duration that Luke had to travel before reaching City L
= 300 ÷ 100
= 3 h

Duration that Brandon had to travel before reaching City L
= 300 ÷ 75
= 4 h

Duration that Brandon took to arrive later than Luke in City L
= 4 - 3
= 1 h

Answer(s): (a) 9.45 a.m.; (b) 1 h