City X and City Y is 518 km apart. Billy left City X for City Y at 9.00 a.m. travelling at an average speed of 74 km/h. Dylan left City X later than Billy and caught up with him at 11.00 a.m. Dylan was travelling at a speed of 111 km/h.

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

(a)
From 9.00 a.m. to 11.00 a.m. = 2 h

Distance that Billy covered when Dylan caught up with Billy
= 2 x 74
= 148 km

Time that Dylan took to travel 148 km
= 148 ÷ 111
= 1¹₃ h

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

Time that Dylan left City X:
1 h 20 min before 11.00 a.m. = 9.40 a.m.

(b)
Remaining distance that they had to cover to reach City Y
= 518 - 148
= 370 km

Duration that Dylan had to travel before reaching City Y
= 370 ÷ 111
= 3¹₃ h

Duration that Billy had to travel before reaching City Y
= 370 ÷ 74
= 5 h

Duration that Billy took to arrive later than Dylan in City Y
= 5 - 3¹₃
= 1²₃ h

Answer(s): (a) 9.40 a.m.; (b) 1²₃ h