City W and City X is 375 km apart. Tom left City W for City X at 11.00 a.m. travelling at an average speed of 75 km/h. Ken left City W later than Tom and caught up with him at 2.00 p.m. Ken was travelling at a speed of 90 km/h.

1. At what time did Ken leave City W?
2. How much later did Tom arrive in City X than Ken? Express your answer in h as a fraction or mixed number.

(a)
From 11.00 a.m. to 2.00 p.m. = 3 h

Distance that Tom covered when Ken caught up with Tom
= 3 x 75
= 225 km

Time that Ken took to travel 225 km
= 225 ÷ 90
= 2¹₂ h

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

Time that Ken left City W:
2 h 30 min before 2.00 p.m. = 11.30 a.m.

(b)
Remaining distance that they had to cover to reach City X
= 375 - 225
= 150 km

Duration that Ken had to travel before reaching City X
= 150 ÷ 90
= 1²₃ h

Duration that Tom had to travel before reaching City X
= 150 ÷ 75
= 2 h

Duration that Tom took to arrive later than Ken in City X
= 2 - 1²₃
= ¹₃ h

Answer(s): (a) 11.30 a.m.; (b) ¹₃ h