City J and City K is 384 km apart. Paul left City J for City K at 7.00 a.m. travelling at an average speed of 64 km/h. Will left City J later than Paul and caught up with him at 9.00 a.m. Will was travelling at a speed of 96 km/h.

1. At what time did Will leave City J?
2. How much later did Paul arrive in City K than Will? Express your answer in h as a fraction or mixed number.

(a)
From 7.00 a.m. to 9.00 a.m. = 2 h

Distance that Paul covered when Will caught up with Paul
= 2 x 64
= 128 km

Time that Will took to travel 128 km
= 128 ÷ 96
= 1¹₃ h

1 h = 60 min
¹₃ h = ¹₃ x 60 = 20 min
1¹₃ h = 1 h 20 min

Time that Will left City J:
1 h 20 min before 9.00 a.m. = 7.40 a.m.

(b)
Remaining distance that they had to cover to reach City K
= 384 - 128
= 256 km

Duration that Will had to travel before reaching City K
= 256 ÷ 96
= 2²₃ h

Duration that Paul had to travel before reaching City K
= 256 ÷ 64
= 4 h

Duration that Paul took to arrive later than Will in City K
= 4 - 2²₃
= 1¹₃ h

Answer(s): (a) 7.40 a.m.; (b) 1¹₃ h