City M and City N is 585 km apart. Simon left City M for City N at 9.00 a.m. travelling at an average speed of 65 km/h. Michael left City M later than Simon and caught up with him at 1.00 p.m. Michael was travelling at a speed of 104 km/h.

1. At what time did Michael leave City M?
2. How much later did Simon arrive in City N than Michael? Express your answer in h as a fraction or mixed number.

(a)
From 9.00 a.m. to 1.00 p.m. = 4 h

Distance that Simon covered when Michael caught up with Simon
= 4 x 65
= 260 km

Time that Michael took to travel 260 km
= 260 ÷ 104
= 2¹₂ h

1 h = 60 min
¹₂ h = ¹₂ x 60 = 30 min
2¹₂ h = 2 h 30 min

Time that Michael left City M:
2 h 30 min before 1.00 p.m. = 10.30 a.m.

(b)
Remaining distance that they had to cover to reach City N
= 585 - 260
= 325 km

Duration that Michael had to travel before reaching City N
= 325 ÷ 104
= 3¹₈ h

Duration that Simon had to travel before reaching City N
= 325 ÷ 65
= 5 h

Duration that Simon took to arrive later than Michael in City N
= 5 - 3¹₈
= 1⁷₈ h

Answer(s): (a) 10.30 a.m.; (b) 1⁷₈ h