City J and City K is 300 km apart. Archie left City J for City K at 11.00 a.m. travelling at an average speed of 60 km/h. Harry left City J later than Archie and caught up with him at 1.00 p.m. Harry was travelling at a speed of 96 km/h.

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

(a)
From 11.00 a.m. to 1.00 p.m. = 2 h

Distance that Archie covered when Harry caught up with Archie
= 2 x 60
= 120 km

Time that Harry took to travel 120 km
= 120 ÷ 96
= 1¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
1¹₄ h = 1 h 15 min

Time that Harry left City J:
1 h 15 min before 1.00 p.m. = 11.45 a.m.

(b)
Remaining distance that they had to cover to reach City K
= 300 - 120
= 180 km

Duration that Harry had to travel before reaching City K
= 180 ÷ 96
= 1⁷₈ h

Duration that Archie had to travel before reaching City K
= 180 ÷ 60
= 3 h

Duration that Archie took to arrive later than Harry in City K
= 3 - 1⁷₈
= 1¹₈ h

Answer(s): (a) 11.45 a.m.; (b) 1¹₈ h