City U and City V is 390 km apart. Cole left City U for City V at 9.00 a.m. travelling at an average speed of 65 km/h. Ethan left City U later than Cole and caught up with him at 12.00 p.m. Ethan was travelling at a speed of 117 km/h.

1. At what time did Ethan leave City U?
2. How much later did Cole arrive in City V than Ethan? 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 Cole covered when Ethan caught up with Cole
= 3 x 65
= 195 km

Time that Ethan took to travel 195 km
= 195 ÷ 117
= 1²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
1²₃ h = 1 h 40 min

Time that Ethan left City U:
1 h 40 min before 12.00 p.m. = 10.20 a.m.

(b)
Remaining distance that they had to cover to reach City V
= 390 - 195
= 195 km

Duration that Ethan had to travel before reaching City V
= 195 ÷ 117
= 1²₃ h

Duration that Cole had to travel before reaching City V
= 195 ÷ 65
= 3 h

Duration that Cole took to arrive later than Ethan in City V
= 3 - 1²₃
= 1¹₃ h

Answer(s): (a) 10.20 a.m.; (b) 1¹₃ h