City J and City K is 648 km apart. Jack left City J for City K at 10.00 a.m. travelling at an average speed of 72 km/h. Nick left City J later than Jack and caught up with him at 2.00 p.m. Nick was travelling at a speed of 108 km/h.

1. At what time did Nick leave City J?
2. How much later did Jack arrive in City K than Nick? 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 Jack covered when Nick caught up with Jack
= 4 x 72
= 288 km

Time that Nick took to travel 288 km
= 288 ÷ 108
= 2²₃ h

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

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

(b)
Remaining distance that they had to cover to reach City K
= 648 - 288
= 360 km

Duration that Nick had to travel before reaching City K
= 360 ÷ 108
= 3¹₃ h

Duration that Jack had to travel before reaching City K
= 360 ÷ 72
= 5 h

Duration that Jack took to arrive later than Nick in City K
= 5 - 3¹₃
= 1²₃ h

Answer(s): (a) 11.20 a.m.; (b) 1²₃ h