City X and City Y is 640 km apart. Caden left City X for City Y at 7.00 a.m. travelling at an average speed of 80 km/h. Ethan left City X later than Caden and caught up with him at 10.00 a.m. Ethan was travelling at a speed of 90 km/h.

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

(a)
From 7.00 a.m. to 10.00 a.m. = 3 h

Distance that Caden covered when Ethan caught up with Caden
= 3 x 80
= 240 km

Time that Ethan took to travel 240 km
= 240 ÷ 90
= 2²₃ h

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

Time that Ethan left City X:
2 h 40 min before 10.00 a.m. = 7.20 a.m.

(b)
Remaining distance that they had to cover to reach City Y
= 640 - 240
= 400 km

Duration that Ethan had to travel before reaching City Y
= 400 ÷ 90
= 4⁴₉ h

Duration that Caden had to travel before reaching City Y
= 400 ÷ 80
= 5 h

Duration that Caden took to arrive later than Ethan in City Y
= 5 - 4⁴₉
= ⁵₉ h

Answer(s): (a) 7.20 a.m.; (b) ⁵₉ h