City N and City P is 612 km apart. Oliver left City N for City P at 9.00 a.m. travelling at an average speed of 68 km/h. Daniel left City N later than Oliver and caught up with him at 1.00 p.m. Daniel was travelling at a speed of 102 km/h.

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

(a)
From 9.00 a.m. to 1.00 p.m. = 4 h

Distance that Oliver covered when Daniel caught up with Oliver
= 4 x 68
= 272 km

Time that Daniel took to travel 272 km
= 272 ÷ 102
= 2²₃ h

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

Time that Daniel left City N:
2 h 40 min before 1.00 p.m. = 10.20 a.m.

(b)
Remaining distance that they had to cover to reach City P
= 612 - 272
= 340 km

Duration that Daniel had to travel before reaching City P
= 340 ÷ 102
= 3¹₃ h

Duration that Oliver had to travel before reaching City P
= 340 ÷ 68
= 5 h

Duration that Oliver took to arrive later than Daniel in City P
= 5 - 3¹₃
= 1²₃ h

Answer(s): (a) 10.20 a.m.; (b) 1²₃ h