City Y and City Z is 384 km apart. Zane left City Y for City Z at 11.00 a.m. travelling at an average speed of 64 km/h. Rael left City Y later than Zane and caught up with him at 1.00 p.m. Rael was travelling at a speed of 96 km/h.

1. At what time did Rael leave City Y?
2. How much later did Zane arrive in City Z than Rael? 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 Zane covered when Rael caught up with Zane
= 2 x 64
= 128 km

Time that Rael took to travel 128 km
= 128 ÷ 96
= 1¹₃ h

1 h = 60 min
¹₃ h = ¹₃ x 60 = 20 min
1¹₃ h = 1 h 20 min

Time that Rael left City Y:
1 h 20 min before 1.00 p.m. = 11.40 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 384 - 128
= 256 km

Duration that Rael had to travel before reaching City Z
= 256 ÷ 96
= 2²₃ h

Duration that Zane had to travel before reaching City Z
= 256 ÷ 64
= 4 h

Duration that Zane took to arrive later than Rael in City Z
= 4 - 2²₃
= 1¹₃ h

Answer(s): (a) 11.40 a.m.; (b) 1¹₃ h