City P and City Q is 420 km apart. Bryan left City P for City Q at 8.00 a.m. travelling at an average speed of 60 km/h. Xavier left City P later than Bryan and caught up with him at 12.00 p.m. Xavier was travelling at a speed of 96 km/h.

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

(a)
From 8.00 a.m. to 12.00 p.m. = 4 h

Distance that Bryan covered when Xavier caught up with Bryan
= 4 x 60
= 240 km

Time that Xavier took to travel 240 km
= 240 ÷ 96
= 2¹₂ h

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

Time that Xavier left City P:
2 h 30 min before 12.00 p.m. = 9.30 a.m.

(b)
Remaining distance that they had to cover to reach City Q
= 420 - 240
= 180 km

Duration that Xavier had to travel before reaching City Q
= 180 ÷ 96
= 1⁷₈ h

Duration that Bryan had to travel before reaching City Q
= 180 ÷ 60
= 3 h

Duration that Bryan took to arrive later than Xavier in City Q
= 3 - 1⁷₈
= 1¹₈ h

Answer(s): (a) 9.30 a.m.; (b) 1¹₈ h