City W and City X is 350 km apart. Tom left City W for City X at 7.00 a.m. travelling at an average speed of 70 km/h. Xavier left City W later than Tom and caught up with him at 10.00 a.m. Xavier was travelling at a speed of 84 km/h.

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

(a)
From 7.00 a.m. to 10.00 a.m. = 3 h

Distance that Tom covered when Xavier caught up with Tom
= 3 x 70
= 210 km

Time that Xavier took to travel 210 km
= 210 ÷ 84
= 2¹₂ h

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

Time that Xavier left City W:
2 h 30 min before 10.00 a.m. = 7.30 a.m.

(b)
Remaining distance that they had to cover to reach City X
= 350 - 210
= 140 km

Duration that Xavier had to travel before reaching City X
= 140 ÷ 84
= 1²₃ h

Duration that Tom had to travel before reaching City X
= 140 ÷ 70
= 2 h

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

Answer(s): (a) 7.30 a.m.; (b) ¹₃ h