City T and City U is 380 km apart. Ethan left City T for City U at 10.00 a.m. travelling at an average speed of 76 km/h. Dylan left City T later than Ethan and caught up with him at 12.00 p.m. Dylan was travelling at a speed of 96 km/h.

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

(a)
From 10.00 a.m. to 12.00 p.m. = 2 h

Distance that Ethan covered when Dylan caught up with Ethan
= 2 x 76
= 152 km

Time that Dylan 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 Dylan left City T:
1 h 35 min before 12.00 p.m. = 10.25 a.m.

(b)
Remaining distance that they had to cover to reach City U
= 380 - 152
= 228 km

Duration that Dylan had to travel before reaching City U
= 228 ÷ 96
= 2³₈ h

Duration that Ethan had to travel before reaching City U
= 228 ÷ 76
= 3 h

Duration that Ethan took to arrive later than Dylan in City U
= 3 - 2³₈
= ⁵₈ h

Answer(s): (a) 10.25 a.m.; (b) ⁵₈ h