City B and City C is 280 km apart. Lee left City B for City C at 11.00 a.m. travelling at an average speed of 70 km/h. Luke left City B later than Lee and caught up with him at 1.00 p.m. Luke was travelling at a speed of 112 km/h.

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

(a)
From 11.00 a.m. to 1.00 p.m. = 2 h

Distance that Lee covered when Luke caught up with Lee
= 2 x 70
= 140 km

Time that Luke took to travel 140 km
= 140 ÷ 112
= 1¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
1¹₄ h = 1 h 15 min

Time that Luke left City B:
1 h 15 min before 1.00 p.m. = 11.45 a.m.

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

Duration that Luke had to travel before reaching City C
= 140 ÷ 112
= 1¹₄ h

Duration that Lee had to travel before reaching City C
= 140 ÷ 70
= 2 h

Duration that Lee took to arrive later than Luke in City C
= 2 - 1¹₄
= ³₄ h

Answer(s): (a) 11.45 a.m.; (b) ³₄ h