City Y and City Z is 315 km apart. Vaidev left City Y for City Z at 11.00 a.m. travelling at an average speed of 63 km/h. Gabriel left City Y later than Vaidev and caught up with him at 1.00 p.m. Gabriel was travelling at a speed of 72 km/h.

1. At what time did Gabriel leave City Y?
2. How much later did Vaidev arrive in City Z than Gabriel? Express your answer in h as a fraction or mixed number.

(a)
From 11.00 a.m. to 1.00 p.m. = 2 h

Distance that Vaidev covered when Gabriel caught up with Vaidev
= 2 x 63
= 126 km

Time that Gabriel took to travel 126 km
= 126 ÷ 72
= 1³₄ h

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

Time that Gabriel left City Y:
1 h 45 min before 1.00 p.m. = 11.15 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 315 - 126
= 189 km

Duration that Gabriel had to travel before reaching City Z
= 189 ÷ 72
= 2⁵₈ h

Duration that Vaidev had to travel before reaching City Z
= 189 ÷ 63
= 3 h

Duration that Vaidev took to arrive later than Gabriel in City Z
= 3 - 2⁵₈
= ³₈ h

Answer(s): (a) 11.15 a.m.; (b) ³₈ h