City Z and City A is 240 km apart. Archie left City Z for City A at 10.00 a.m. travelling at an average speed of 60 km/h. Tim left City Z later than Archie and caught up with him at 12.00 p.m. Tim was travelling at a speed of 96 km/h.

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

(a)
From 10.00 a.m. to 12.00 p.m. = 2 h

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

Time that Tim 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 Tim left City Z:
1 h 15 min before 12.00 p.m. = 10.45 a.m.

(b)
Remaining distance that they had to cover to reach City A
= 240 - 120
= 120 km

Duration that Tim had to travel before reaching City A
= 120 ÷ 96
= 1¹₄ h

Duration that Archie had to travel before reaching City A
= 120 ÷ 60
= 2 h

Duration that Archie took to arrive later than Tim in City A
= 2 - 1¹₄
= ³₄ h

Answer(s): (a) 10.45 a.m.; (b) ³₄ h