City P and City Q is 528 km apart. Jack left City P for City Q at 8.00 a.m. travelling at an average speed of 66 km/h. Daniel left City P later than Jack and caught up with him at 11.00 a.m. Daniel was travelling at a speed of 72 km/h.

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

(a)
From 8.00 a.m. to 11.00 a.m. = 3 h

Distance that Jack covered when Daniel caught up with Jack
= 3 x 66
= 198 km

Time that Daniel took to travel 198 km
= 198 ÷ 72
= 2³₄ h

1 h = 60 min
³₄ h = ³₄ x 60 = 45 min
2³₄ h = 2 h 45 min

Time that Daniel left City P:
2 h 45 min before 11.00 a.m. = 8.15 a.m.

(b)
Remaining distance that they had to cover to reach City Q
= 528 - 198
= 330 km

Duration that Daniel had to travel before reaching City Q
= 330 ÷ 72
= 4⁷₁₂ h

Duration that Jack had to travel before reaching City Q
= 330 ÷ 66
= 5 h

Duration that Jack took to arrive later than Daniel in City Q
= 5 - 4⁷₁₂
= ⁵₁₂ h

Answer(s): (a) 8.15 a.m.; (b) ⁵₁₂ h