City X and City Y is 441 km apart. Perry left City X for City Y at 9.00 a.m. travelling at an average speed of 63 km/h. Fabian left City X later than Perry and caught up with him at 12.00 p.m. Fabian was travelling at a speed of 108 km/h.

1. At what time did Fabian leave City X?
2. How much later did Perry arrive in City Y than Fabian? 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 Perry covered when Fabian caught up with Perry
= 3 x 63
= 189 km

Time that Fabian took to travel 189 km
= 189 ÷ 108
= 1³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
1³₄ h = 1 h 45 min

Time that Fabian left City X:
1 h 45 min before 12.00 p.m. = 10.15 a.m.

(b)
Remaining distance that they had to cover to reach City Y
= 441 - 189
= 252 km

Duration that Fabian had to travel before reaching City Y
= 252 ÷ 108
= 2¹₃ h

Duration that Perry had to travel before reaching City Y
= 252 ÷ 63
= 4 h

Duration that Perry took to arrive later than Fabian in City Y
= 4 - 2¹₃
= 1²₃ h

Answer(s): (a) 10.15 a.m.; (b) 1²₃ h