City M and City N is 345 km apart. Cole left City M for City N at 7.00 a.m. travelling at an average speed of 69 km/h. Simon left City M later than Cole and caught up with him at 9.00 a.m. Simon was travelling at a speed of 92 km/h.

1. At what time did Simon leave City M?
2. How much later did Cole arrive in City N than Simon? 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 Cole covered when Simon caught up with Cole
= 2 x 69
= 138 km

Time that Simon took to travel 138 km
= 138 ÷ 92
= 1¹₂ h

1 h = 60 min
¹₂ h = ¹₂ x 60 = 30 min
1¹₂ h = 1 h 30 min

Time that Simon left City M:
1 h 30 min before 9.00 a.m. = 7.30 a.m.

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

Duration that Simon had to travel before reaching City N
= 207 ÷ 92
= 2¹₄ h

Duration that Cole had to travel before reaching City N
= 207 ÷ 69
= 3 h

Duration that Cole took to arrive later than Simon in City N
= 3 - 2¹₄
= ³₄ h

Answer(s): (a) 7.30 a.m.; (b) ³₄ h