City J and City K is 320 km apart. Zane left City J for City K at 7.00 a.m. travelling at an average speed of 80 km/h. Paul left City J later than Zane and caught up with him at 9.00 a.m. Paul was travelling at a speed of 96 km/h.

1. At what time did Paul leave City J?
2. How much later did Zane arrive in City K than Paul? 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 Zane covered when Paul caught up with Zane
= 2 x 80
= 160 km

Time that Paul took to travel 160 km
= 160 ÷ 96
= 1²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
1²₃ h = 1 h 40 min

Time that Paul left City J:
1 h 40 min before 9.00 a.m. = 7.20 a.m.

(b)
Remaining distance that they had to cover to reach City K
= 320 - 160
= 160 km

Duration that Paul had to travel before reaching City K
= 160 ÷ 96
= 1²₃ h

Duration that Zane had to travel before reaching City K
= 160 ÷ 80
= 2 h

Duration that Zane took to arrive later than Paul in City K
= 2 - 1²₃
= ¹₃ h

Answer(s): (a) 7.20 a.m.; (b) ¹₃ h