City N and City P is 624 km apart. Xavier left City N for City P at 10.00 a.m. travelling at an average speed of 78 km/h. Vincent left City N later than Xavier and caught up with him at 1.00 p.m. Vincent was travelling at a speed of 104 km/h.

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

(a)
From 10.00 a.m. to 1.00 p.m. = 3 h

Distance that Xavier covered when Vincent caught up with Xavier
= 3 x 78
= 234 km

Time that Vincent took to travel 234 km
= 234 ÷ 104
= 2¹₄ h

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

Time that Vincent left City N:
2 h 15 min before 1.00 p.m. = 10.45 a.m.

(b)
Remaining distance that they had to cover to reach City P
= 624 - 234
= 390 km

Duration that Vincent had to travel before reaching City P
= 390 ÷ 104
= 3³₄ h

Duration that Xavier had to travel before reaching City P
= 390 ÷ 78
= 5 h

Duration that Xavier took to arrive later than Vincent in City P
= 5 - 3³₄
= 1¹₄ h

Answer(s): (a) 10.45 a.m.; (b) 1¹₄ h