City Y and City Z is 450 km apart. Tommy left City Y for City Z at 8.00 a.m. travelling at an average speed of 75 km/h. Riordan left City Y later than Tommy and caught up with him at 10.00 a.m. Riordan was travelling at a speed of 90 km/h.

1. At what time did Riordan leave City Y?
2. How much later did Tommy arrive in City Z than Riordan? 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 Tommy covered when Riordan caught up with Tommy
= 2 x 75
= 150 km

Time that Riordan took to travel 150 km
= 150 ÷ 90
= 1²₃ h

1 h = 60 min
²₃ h = ²₃ x 60 = 40 min
1²₃ h = 1 h 40 min

Time that Riordan left City Y:
1 h 40 min before 10.00 a.m. = 8.20 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 450 - 150
= 300 km

Duration that Riordan had to travel before reaching City Z
= 300 ÷ 90
= 3¹₃ h

Duration that Tommy had to travel before reaching City Z
= 300 ÷ 75
= 4 h

Duration that Tommy took to arrive later than Riordan in City Z
= 4 - 3¹₃
= ²₃ h

Answer(s): (a) 8.20 a.m.; (b) ²₃ h