City B and City C is 490 km apart. Luke left City B for City C at 11.00 a.m. travelling at an average speed of 70 km/h. Howard left City B later than Luke and caught up with him at 1.00 p.m. Howard was travelling at a speed of 112 km/h.

1. At what time did Howard leave City B?
2. How much later did Luke arrive in City C than Howard? 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 Luke covered when Howard caught up with Luke
= 2 x 70
= 140 km

Time that Howard 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 Howard 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
= 490 - 140
= 350 km

Duration that Howard had to travel before reaching City C
= 350 ÷ 112
= 3¹₈ h

Duration that Luke had to travel before reaching City C
= 350 ÷ 70
= 5 h

Duration that Luke took to arrive later than Howard in City C
= 5 - 3¹₈
= 1⁷₈ h

Answer(s): (a) 11.45 a.m.; (b) 1⁷₈ h