City Y and City Z is 370 km apart. Vincent left City Y for City Z at 8.00 a.m. travelling at an average speed of 74 km/h. Howard left City Y later than Vincent and caught up with him at 10.00 a.m. Howard was travelling at a speed of 111 km/h.

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

(a)
From 8.00 a.m. to 10.00 a.m. = 2 h

Distance that Vincent covered when Howard caught up with Vincent
= 2 x 74
= 148 km

Time that Howard 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 Howard left City Y:
1 h 20 min before 10.00 a.m. = 8.40 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 370 - 148
= 222 km

Duration that Howard had to travel before reaching City Z
= 222 ÷ 111
= 2 h

Duration that Vincent had to travel before reaching City Z
= 222 ÷ 74
= 3 h

Duration that Vincent took to arrive later than Howard in City Z
= 3 - 2
= 1 h

Answer(s): (a) 8.40 a.m.; (b) 1 h