City T and City U is 304 km apart. Reggie left City T for City U at 11.00 a.m. travelling at an average speed of 76 km/h. Billy left City T later than Reggie and caught up with him at 1.00 p.m. Billy was travelling at a speed of 96 km/h.

1. At what time did Billy leave City T?
2. How much later did Reggie arrive in City U than Billy? Express your answer in h as a fraction or mixed number.

(a)
From 11.00 a.m. to 1.00 p.m. = 2 h

Distance that Reggie covered when Billy caught up with Reggie
= 2 x 76
= 152 km

Time that Billy took to travel 152 km
= 152 ÷ 96
= 1⁷₁₂ h

1 h = 60 min
⁷₁₂ h = ⁷₁₂ x 60 = 35 min
1⁷₁₂ h = 1 h 35 min

Time that Billy left City T:
1 h 35 min before 1.00 p.m. = 11.25 a.m.

(b)
Remaining distance that they had to cover to reach City U
= 304 - 152
= 152 km

Duration that Billy had to travel before reaching City U
= 152 ÷ 96
= 1⁷₁₂ h

Duration that Reggie had to travel before reaching City U
= 152 ÷ 76
= 2 h

Duration that Reggie took to arrive later than Billy in City U
= 2 - 1⁷₁₂
= ⁵₁₂ h

Answer(s): (a) 11.25 a.m.; (b) ⁵₁₂ h