City X and City Y is 434 km apart. Reggie left City X for City Y at 10.00 a.m. travelling at an average speed of 62 km/h. Neave left City X later than Reggie and caught up with him at 2.00 p.m. Neave was travelling at a speed of 93 km/h.

1. At what time did Neave leave City X?
2. How much later did Reggie arrive in City Y than Neave? Express your answer in h as a fraction or mixed number.

(a)
From 10.00 a.m. to 2.00 p.m. = 4 h

Distance that Reggie covered when Neave caught up with Reggie
= 4 x 62
= 248 km

Time that Neave took to travel 248 km
= 248 ÷ 93
= 2²₃ h

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

Time that Neave left City X:
2 h 40 min before 2.00 p.m. = 11.20 a.m.

(b)
Remaining distance that they had to cover to reach City Y
= 434 - 248
= 186 km

Duration that Neave had to travel before reaching City Y
= 186 ÷ 93
= 2 h

Duration that Reggie had to travel before reaching City Y
= 186 ÷ 62
= 3 h

Duration that Reggie took to arrive later than Neave in City Y
= 3 - 2
= 1 h

Answer(s): (a) 11.20 a.m.; (b) 1 h