City P and City Q is 648 km apart. Jeremy left City P for City Q at 8.00 a.m. travelling at an average speed of 72 km/h. Neave left City P later than Jeremy and caught up with him at 12.00 p.m. Neave was travelling at a speed of 108 km/h.

1. At what time did Neave leave City P?
2. How much later did Jeremy arrive in City Q than Neave? 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 Jeremy covered when Neave caught up with Jeremy
= 4 x 72
= 288 km

Time that Neave took to travel 288 km
= 288 ÷ 108
= 2²₃ h

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

Time that Neave 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
= 648 - 288
= 360 km

Duration that Neave had to travel before reaching City Q
= 360 ÷ 108
= 3¹₃ h

Duration that Jeremy had to travel before reaching City Q
= 360 ÷ 72
= 5 h

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

Answer(s): (a) 9.20 a.m.; (b) 1²₃ h