City Y and City Z is 612 km apart. Ryan left City Y for City Z at 7.00 a.m. travelling at an average speed of 68 km/h. Ken left City Y later than Ryan and caught up with him at 11.00 a.m. Ken was travelling at a speed of 96 km/h.

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

(a)
From 7.00 a.m. to 11.00 a.m. = 4 h

Distance that Ryan covered when Ken caught up with Ryan
= 4 x 68
= 272 km

Time that Ken took to travel 272 km
= 272 ÷ 96
= 2⁵₆ h

1 h = 60 min
⁵₆ h = ⁵₆ x 60 = 50 min
2⁵₆ h = 2 h 50 min

Time that Ken left City Y:
2 h 50 min before 11.00 a.m. = 8.10 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 612 - 272
= 340 km

Duration that Ken had to travel before reaching City Z
= 340 ÷ 96
= 3¹³₂₄ h

Duration that Ryan had to travel before reaching City Z
= 340 ÷ 68
= 5 h

Duration that Ryan took to arrive later than Ken in City Z
= 5 - 3¹³₂₄
= 1¹¹₂₄ h

Answer(s): (a) 8.10 a.m.; (b) 1¹¹₂₄ h