City Y and City Z is 375 km apart. Caden left City Y for City Z at 8.00 a.m. travelling at an average speed of 75 km/h. Archie left City Y later than Caden and caught up with him at 10.00 a.m. Archie was travelling at a speed of 100 km/h.

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

Time that Archie took to travel 150 km
= 150 ÷ 100
= 1¹₂ h

1 h = 60 min
¹₂ h = ¹₂ x 60 = 30 min
1¹₂ h = 1 h 30 min

Time that Archie left City Y:
1 h 30 min before 10.00 a.m. = 8.30 a.m.

(b)
Remaining distance that they had to cover to reach City Z
= 375 - 150
= 225 km

Duration that Archie had to travel before reaching City Z
= 225 ÷ 100
= 2¹₄ h

Duration that Caden had to travel before reaching City Z
= 225 ÷ 75
= 3 h

Duration that Caden took to arrive later than Archie in City Z
= 3 - 2¹₄
= ³₄ h

Answer(s): (a) 8.30 a.m.; (b) ³₄ h