City N and City P is 300 km apart. Bryan left City N for City P at 9.00 a.m. travelling at an average speed of 75 km/h. Luke left City N later than Bryan and caught up with him at 11.00 a.m. Luke was travelling at a speed of 100 km/h.

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

(a)
From 9.00 a.m. to 11.00 a.m. = 2 h

Distance that Bryan covered when Luke caught up with Bryan
= 2 x 75
= 150 km

Time that Luke took to travel 150 km
= 150 ÷ 100
= 1¹₂ h

1 h = 60 min
¹₂ h = ¹₂ x 60 = 30 min
1¹₂ h = 1 h 30 min

Time that Luke left City N:
1 h 30 min before 11.00 a.m. = 9.30 a.m.

(b)
Remaining distance that they had to cover to reach City P
= 300 - 150
= 150 km

Duration that Luke had to travel before reaching City P
= 150 ÷ 100
= 1¹₂ h

Duration that Bryan had to travel before reaching City P
= 150 ÷ 75
= 2 h

Duration that Bryan took to arrive later than Luke in City P
= 2 - 1¹₂
= ¹₂ h

Answer(s): (a) 9.30 a.m.; (b) ¹₂ h