City P and City Q is 612 km apart. Charlie left City P for City Q at 8.00 a.m. travelling at an average speed of 68 km/h. Julian left City P later than Charlie and caught up with him at 12.00 p.m. Julian was travelling at a speed of 102 km/h.

1. At what time did Julian leave City P?
2. How much later did Charlie arrive in City Q than Julian? 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 Charlie covered when Julian caught up with Charlie
= 4 x 68
= 272 km

Time that Julian took to travel 272 km
= 272 ÷ 102
= 2²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
2²₃ h = 2 h 40 min

Time that Julian left City P:
2 h 40 min before 12.00 p.m. = 9.20 a.m.

(b)
Remaining distance that they had to cover to reach City Q
= 612 - 272
= 340 km

Duration that Julian had to travel before reaching City Q
= 340 ÷ 102
= 3¹₃ h

Duration that Charlie had to travel before reaching City Q
= 340 ÷ 68
= 5 h

Duration that Charlie took to arrive later than Julian in City Q
= 5 - 3¹₃
= 1²₃ h

Answer(s): (a) 9.20 a.m.; (b) 1²₃ h