City T and City U is 616 km apart. Ivan left City T for City U at 11.00 a.m. travelling at an average speed of 77 km/h. Julian left City T later than Ivan and caught up with him at 2.00 p.m. Julian was travelling at a speed of 84 km/h.

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

(a)
From 11.00 a.m. to 2.00 p.m. = 3 h

Distance that Ivan covered when Julian caught up with Ivan
= 3 x 77
= 231 km

Time that Julian took to travel 231 km
= 231 ÷ 84
= 2³₄ h

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

Time that Julian left City T:
2 h 45 min before 2.00 p.m. = 11.15 a.m.

(b)
Remaining distance that they had to cover to reach City U
= 616 - 231
= 385 km

Duration that Julian had to travel before reaching City U
= 385 ÷ 84
= 4⁷₁₂ h

Duration that Ivan had to travel before reaching City U
= 385 ÷ 77
= 5 h

Duration that Ivan took to arrive later than Julian in City U
= 5 - 4⁷₁₂
= ⁵₁₂ h

Answer(s): (a) 11.15 a.m.; (b) ⁵₁₂ h