City N and City P is 496 km apart. George left City N for City P at 8.00 a.m. travelling at an average speed of 62 km/h. Luke left City N later than George and caught up with him at 12.00 p.m. Luke was travelling at a speed of 93 km/h.

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

(a)
From 8.00 a.m. to 12.00 p.m. = 4 h

Distance that George covered when Luke caught up with George
= 4 x 62
= 248 km

Time that Luke took to travel 248 km
= 248 ÷ 93
= 2²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
2²₃ h = 2 h 40 min

Time that Luke left City N:
2 h 40 min before 12.00 p.m. = 9.20 a.m.

(b)
Remaining distance that they had to cover to reach City P
= 496 - 248
= 248 km

Duration that Luke had to travel before reaching City P
= 248 ÷ 93
= 2²₃ h

Duration that George had to travel before reaching City P
= 248 ÷ 62
= 4 h

Duration that George took to arrive later than Luke in City P
= 4 - 2²₃
= 1¹₃ h

Answer(s): (a) 9.20 a.m.; (b) 1¹₃ h