City Y and City Z is 462 km apart. Vaidev left City Y for City Z at 8.00 a.m. travelling at an average speed of 77 km/h. Will left City Y later than Vaidev and caught up with him at 11.00 a.m. Will was travelling at a speed of 84 km/h.

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

(a)
From 8.00 a.m. to 11.00 a.m. = 3 h

Distance that Vaidev covered when Will caught up with Vaidev
= 3 x 77
= 231 km

Time that Will took to travel 231 km
= 231 ÷ 84
= 2³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
2³₄ h = 2 h 45 min

Time that Will left City Y:
2 h 45 min before 11.00 a.m. = 8.15 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 462 - 231
= 231 km

Duration that Will had to travel before reaching City Z
= 231 ÷ 84
= 2³₄ h

Duration that Vaidev had to travel before reaching City Z
= 231 ÷ 77
= 3 h

Duration that Vaidev took to arrive later than Will in City Z
= 3 - 2³₄
= ¹₄ h

Answer(s): (a) 8.15 a.m.; (b) ¹₄ h