City N and City P is 432 km apart. Glen left City N for City P at 8.00 a.m. travelling at an average speed of 72 km/h. Archie left City N later than Glen and caught up with him at 11.00 a.m. Archie was travelling at a speed of 81 km/h.

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

(a)
From 8.00 a.m. to 11.00 a.m. = 3 h

Distance that Glen covered when Archie caught up with Glen
= 3 x 72
= 216 km

Time that Archie 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 Archie left City N:
2 h 40 min before 11.00 a.m. = 8.20 a.m.

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

Duration that Archie had to travel before reaching City P
= 216 ÷ 81
= 2²₃ h

Duration that Glen had to travel before reaching City P
= 216 ÷ 72
= 3 h

Duration that Glen took to arrive later than Archie in City P
= 3 - 2²₃
= ¹₃ h

Answer(s): (a) 8.20 a.m.; (b) ¹₃ h