City X and City Y is 264 km apart. Vincent left City X for City Y at 7.00 a.m. travelling at an average speed of 66 km/h. Mark left City X later than Vincent and caught up with him at 9.00 a.m. Mark was travelling at a speed of 99 km/h.

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

(a)
From 7.00 a.m. to 9.00 a.m. = 2 h

Distance that Vincent covered when Mark caught up with Vincent
= 2 x 66
= 132 km

Time that Mark took to travel 132 km
= 132 ÷ 99
= 1¹₃ h

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

Time that Mark left City X:
1 h 20 min before 9.00 a.m. = 7.40 a.m.

(b)
Remaining distance that they had to cover to reach City Y
= 264 - 132
= 132 km

Duration that Mark had to travel before reaching City Y
= 132 ÷ 99
= 1¹₃ h

Duration that Vincent had to travel before reaching City Y
= 132 ÷ 66
= 2 h

Duration that Vincent took to arrive later than Mark in City Y
= 2 - 1¹₃
= ²₃ h

Answer(s): (a) 7.40 a.m.; (b) ²₃ h