City C and City D is 420 km apart. Sam left City C for City D at 7.00 a.m. travelling at an average speed of 70 km/h. Jeremy left City C later than Sam and caught up with him at 11.00 a.m. Jeremy was travelling at a speed of 112 km/h.

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

(a)
From 7.00 a.m. to 11.00 a.m. = 4 h

Distance that Sam covered when Jeremy caught up with Sam
= 4 x 70
= 280 km

Time that Jeremy took to travel 280 km
= 280 ÷ 112
= 2¹₂ h

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

Time that Jeremy left City C:
2 h 30 min before 11.00 a.m. = 8.30 a.m.

(b)
Remaining distance that they had to cover to reach City D
= 420 - 280
= 140 km

Duration that Jeremy had to travel before reaching City D
= 140 ÷ 112
= 1¹₄ h

Duration that Sam had to travel before reaching City D
= 140 ÷ 70
= 2 h

Duration that Sam took to arrive later than Jeremy in City D
= 2 - 1¹₄
= ³₄ h

Answer(s): (a) 8.30 a.m.; (b) ³₄ h