City X and City Y is 420 km apart. Elijah left City X for City Y at 9.00 a.m. travelling at an average speed of 60 km/h. Reggie left City X later than Elijah and caught up with him at 12.00 p.m. Reggie was travelling at a speed of 72 km/h.

1. At what time did Reggie leave City X?
2. How much later did Elijah arrive in City Y than Reggie? 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 Elijah covered when Reggie caught up with Elijah
= 3 x 60
= 180 km

Time that Reggie took to travel 180 km
= 180 ÷ 72
= 2¹₂ h

1 h = 60 min
¹₂ h = ¹₂ x 60 = 30 min
2¹₂ h = 2 h 30 min

Time that Reggie left City X:
2 h 30 min before 12.00 p.m. = 9.30 a.m.

(b)
Remaining distance that they had to cover to reach City Y
= 420 - 180
= 240 km

Duration that Reggie had to travel before reaching City Y
= 240 ÷ 72
= 3¹₃ h

Duration that Elijah had to travel before reaching City Y
= 240 ÷ 60
= 4 h

Duration that Elijah took to arrive later than Reggie in City Y
= 4 - 3¹₃
= ²₃ h

Answer(s): (a) 9.30 a.m.; (b) ²₃ h