City Y and City Z is 512 km apart. Gabriel left City Y for City Z at 11.00 a.m. travelling at an average speed of 64 km/h. Neave left City Y later than Gabriel and caught up with him at 2.00 p.m. Neave was travelling at a speed of 72 km/h.

1. At what time did Neave leave City Y?
2. How much later did Gabriel arrive in City Z than Neave? 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 Gabriel covered when Neave caught up with Gabriel
= 3 x 64
= 192 km

Time that Neave took to travel 192 km
= 192 ÷ 72
= 2²₃ h

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

Time that Neave left City Y:
2 h 40 min before 2.00 p.m. = 11.20 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 512 - 192
= 320 km

Duration that Neave had to travel before reaching City Z
= 320 ÷ 72
= 4⁴₉ h

Duration that Gabriel had to travel before reaching City Z
= 320 ÷ 64
= 5 h

Duration that Gabriel took to arrive later than Neave in City Z
= 5 - 4⁴₉
= ⁵₉ h

Answer(s): (a) 11.20 a.m.; (b) ⁵₉ h