City M and City N is 360 km apart. David left City M for City N at 9.00 a.m. travelling at an average speed of 60 km/h. Fred left City M later than David and caught up with him at 12.00 p.m. Fred was travelling at a speed of 80 km/h.

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

(a)
From 9.00 a.m. to 12.00 p.m. = 3 h

Distance that David covered when Fred caught up with David
= 3 x 60
= 180 km

Time that Fred took to travel 180 km
= 180 ÷ 80
= 2¹₄ h

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

Time that Fred left City M:
2 h 15 min before 12.00 p.m. = 9.45 a.m.

(b)
Remaining distance that they had to cover to reach City N
= 360 - 180
= 180 km

Duration that Fred had to travel before reaching City N
= 180 ÷ 80
= 2¹₄ h

Duration that David had to travel before reaching City N
= 180 ÷ 60
= 3 h

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

Answer(s): (a) 9.45 a.m.; (b) ³₄ h