City P and City Q is 462 km apart. Caden left City P for City Q at 7.00 a.m. travelling at an average speed of 66 km/h. Gabriel left City P later than Caden and caught up with him at 10.00 a.m. Gabriel was travelling at a speed of 88 km/h.

1. At what time did Gabriel leave City P?
2. How much later did Caden arrive in City Q than Gabriel? Express your answer in h as a fraction or mixed number.

(a)
From 7.00 a.m. to 10.00 a.m. = 3 h

Distance that Caden covered when Gabriel caught up with Caden
= 3 x 66
= 198 km

Time that Gabriel took to travel 198 km
= 198 ÷ 88
= 2¹₄ h

1 h = 60 min
¹₄ h = ¹₄ x 60 = 15 min
2¹₄ h = 2 h 15 min

Time that Gabriel left City P:
2 h 15 min before 10.00 a.m. = 7.45 a.m.

(b)
Remaining distance that they had to cover to reach City Q
= 462 - 198
= 264 km

Duration that Gabriel had to travel before reaching City Q
= 264 ÷ 88
= 3 h

Duration that Caden had to travel before reaching City Q
= 264 ÷ 66
= 4 h

Duration that Caden took to arrive later than Gabriel in City Q
= 4 - 3
= 1 h

Answer(s): (a) 7.45 a.m.; (b) 1 h