City P and City Q is 432 km apart. Flynn left City P for City Q at 9.00 a.m. travelling at an average speed of 72 km/h. Zeph left City P later than Flynn and caught up with him at 12.00 p.m. Zeph was travelling at a speed of 81 km/h.

1. At what time did Zeph leave City P?
2. How much later did Flynn arrive in City Q than Zeph? 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 Flynn covered when Zeph caught up with Flynn
= 3 x 72
= 216 km

Time that Zeph took to travel 216 km
= 216 ÷ 81
= 2²₃ h

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

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

(b)
Remaining distance that they had to cover to reach City Q
= 432 - 216
= 216 km

Duration that Zeph had to travel before reaching City Q
= 216 ÷ 81
= 2²₃ h

Duration that Flynn had to travel before reaching City Q
= 216 ÷ 72
= 3 h

Duration that Flynn took to arrive later than Zeph in City Q
= 3 - 2²₃
= ¹₃ h

Answer(s): (a) 9.20 a.m.; (b) ¹₃ h