City L and City M is 455 km apart. Oscar left City L for City M at 10.00 a.m. travelling at an average speed of 65 km/h. Oliver left City L later than Oscar and caught up with him at 1.00 p.m. Oliver was travelling at a speed of 78 km/h.

1. At what time did Oliver leave City L?
2. How much later did Oscar arrive in City M than Oliver? Express your answer in h as a fraction or mixed number.

(a)
From 10.00 a.m. to 1.00 p.m. = 3 h

Distance that Oscar covered when Oliver caught up with Oscar
= 3 x 65
= 195 km

Time that Oliver took to travel 195 km
= 195 ÷ 78
= 2¹₂ h

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

Time that Oliver left City L:
2 h 30 min before 1.00 p.m. = 10.30 a.m.

(b)
Remaining distance that they had to cover to reach City M
= 455 - 195
= 260 km

Duration that Oliver had to travel before reaching City M
= 260 ÷ 78
= 3¹₃ h

Duration that Oscar had to travel before reaching City M
= 260 ÷ 65
= 4 h

Duration that Oscar took to arrive later than Oliver in City M
= 4 - 3¹₃
= ²₃ h

Answer(s): (a) 10.30 a.m.; (b) ²₃ h