City M and City N is 624 km apart. Harry left City M for City N at 9.00 a.m. travelling at an average speed of 78 km/h. Sean left City M later than Harry and caught up with him at 1.00 p.m. Sean was travelling at a speed of 117 km/h.

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

(a)
From 9.00 a.m. to 1.00 p.m. = 4 h

Distance that Harry covered when Sean caught up with Harry
= 4 x 78
= 312 km

Time that Sean took to travel 312 km
= 312 ÷ 117
= 2²₃ h

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

Time that Sean left City M:
2 h 40 min before 1.00 p.m. = 10.20 a.m.

(b)
Remaining distance that they had to cover to reach City N
= 624 - 312
= 312 km

Duration that Sean had to travel before reaching City N
= 312 ÷ 117
= 2²₃ h

Duration that Harry had to travel before reaching City N
= 312 ÷ 78
= 4 h

Duration that Harry took to arrive later than Sean in City N
= 4 - 2²₃
= 1¹₃ h

Answer(s): (a) 10.20 a.m.; (b) 1¹₃ h