City P and City Q is 441 km apart. Harry left City P for City Q at 11.00 a.m. travelling at an average speed of 63 km/h. Carl left City P later than Harry and caught up with him at 2.00 p.m. Carl was travelling at a speed of 108 km/h.

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

Time that Carl 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 Carl left City P:
1 h 45 min before 2.00 p.m. = 12.15 p.m.

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

Duration that Carl had to travel before reaching City Q
= 252 ÷ 108
= 2¹₃ h

Duration that Harry had to travel before reaching City Q
= 252 ÷ 63
= 4 h

Duration that Harry took to arrive later than Carl in City Q
= 4 - 2¹₃
= 1²₃ h

Answer(s): (a) 12.15 p.m.; (b) 1²₃ h