City M and City N is 360 km apart. Warren left City M for City N at 10.00 a.m. travelling at an average speed of 60 km/h. Cole left City M later than Warren and caught up with him at 2.00 p.m. Cole was travelling at a speed of 90 km/h.

1. At what time did Cole leave City M?
2. How much later did Warren arrive in City N than Cole? 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 Warren covered when Cole caught up with Warren
= 4 x 60
= 240 km

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

(b)
Remaining distance that they had to cover to reach City N
= 360 - 240
= 120 km

Duration that Cole had to travel before reaching City N
= 120 ÷ 90
= 1¹₃ h

Duration that Warren had to travel before reaching City N
= 120 ÷ 60
= 2 h

Duration that Warren took to arrive later than Cole in City N
= 2 - 1¹₃
= ²₃ h

Answer(s): (a) 11.20 a.m.; (b) ²₃ h