City N and City P is 441 km apart. Vincent left City N for City P at 9.00 a.m. travelling at an average speed of 63 km/h. Howard left City N later than Vincent and caught up with him at 12.00 p.m. Howard was travelling at a speed of 108 km/h.

1. At what time did Howard leave City N?
2. How much later did Vincent arrive in City P than Howard? 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 Vincent covered when Howard caught up with Vincent
= 3 x 63
= 189 km

Time that Howard took to travel 189 km
= 189 ÷ 108
= 1³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
1³₄ h = 1 h 45 min

Time that Howard left City N:
1 h 45 min before 12.00 p.m. = 10.15 a.m.

(b)
Remaining distance that they had to cover to reach City P
= 441 - 189
= 252 km

Duration that Howard had to travel before reaching City P
= 252 ÷ 108
= 2¹₃ h

Duration that Vincent had to travel before reaching City P
= 252 ÷ 63
= 4 h

Duration that Vincent took to arrive later than Howard in City P
= 4 - 2¹₃
= 1²₃ h

Answer(s): (a) 10.15 a.m.; (b) 1²₃ h