City W and City X is 552 km apart. Sam left City W for City X at 9.00 a.m. travelling at an average speed of 69 km/h. Ivan left City W later than Sam and caught up with him at 12.00 p.m. Ivan was travelling at a speed of 92 km/h.

1. At what time did Ivan leave City W?
2. How much later did Sam arrive in City X than Ivan? 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 Sam covered when Ivan caught up with Sam
= 3 x 69
= 207 km

Time that Ivan took to travel 207 km
= 207 ÷ 92
= 2¹₄ h

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

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

(b)
Remaining distance that they had to cover to reach City X
= 552 - 207
= 345 km

Duration that Ivan had to travel before reaching City X
= 345 ÷ 92
= 3³₄ h

Duration that Sam had to travel before reaching City X
= 345 ÷ 69
= 5 h

Duration that Sam took to arrive later than Ivan in City X
= 5 - 3³₄
= 1¹₄ h

Answer(s): (a) 9.45 a.m.; (b) 1¹₄ h