City B and City C is 345 km apart. Nick left City B for City C at 7.00 a.m. travelling at an average speed of 69 km/h. Tom left City B later than Nick and caught up with him at 10.00 a.m. Tom was travelling at a speed of 92 km/h.

1. At what time did Tom leave City B?
2. How much later did Nick arrive in City C than Tom? Express your answer in h as a fraction or mixed number.

(a)
From 7.00 a.m. to 10.00 a.m. = 3 h

Distance that Nick covered when Tom caught up with Nick
= 3 x 69
= 207 km

Time that Tom took to travel 207 km
= 207 ÷ 92
= 2¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
2¹₄ h = 2 h 15 min

Time that Tom left City B:
2 h 15 min before 10.00 a.m. = 7.45 a.m.

(b)
Remaining distance that they had to cover to reach City C
= 345 - 207
= 138 km

Duration that Tom had to travel before reaching City C
= 138 ÷ 92
= 1¹₂ h

Duration that Nick had to travel before reaching City C
= 138 ÷ 69
= 2 h

Duration that Nick took to arrive later than Tom in City C
= 2 - 1¹₂
= ¹₂ h

Answer(s): (a) 7.45 a.m.; (b) ¹₂ h