City Y and City Z is 462 km apart. Valen left City Y for City Z at 7.00 a.m. travelling at an average speed of 77 km/h. Eric left City Y later than Valen and caught up with him at 10.00 a.m. Eric was travelling at a speed of 84 km/h.

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

(a)
From 7.00 a.m. to 10.00 a.m. = 3 h

Distance that Valen covered when Eric caught up with Valen
= 3 x 77
= 231 km

Time that Eric 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 Eric left City Y:
2 h 45 min before 10.00 a.m. = 7.15 a.m.

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

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

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

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

Answer(s): (a) 7.15 a.m.; (b) ¹₄ h