City W and City X is 320 km apart. Lee left City W for City X at 8.00 a.m. travelling at an average speed of 80 km/h. Archie left City W later than Lee and caught up with him at 10.00 a.m. Archie was travelling at a speed of 96 km/h.

1. At what time did Archie leave City W?
2. How much later did Lee arrive in City X than Archie? Express your answer in h as a fraction or mixed number.

(a)
From 8.00 a.m. to 10.00 a.m. = 2 h

Distance that Lee covered when Archie caught up with Lee
= 2 x 80
= 160 km

Time that Archie 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 Archie left City W:
1 h 40 min before 10.00 a.m. = 8.20 a.m.

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

Duration that Archie had to travel before reaching City X
= 160 ÷ 96
= 1²₃ h

Duration that Lee had to travel before reaching City X
= 160 ÷ 80
= 2 h

Duration that Lee took to arrive later than Archie in City X
= 2 - 1²₃
= ¹₃ h

Answer(s): (a) 8.20 a.m.; (b) ¹₃ h