No ambiguity about the travel time. Kirk orders warp, we see the ship go to warp then Carol Marcus informs Kirk that the Vengeance will still be able to catch up and overtake them.. this takes 30 seconds. Then another 30 seconds whilst the Vengeance catches them and another 30 seconds of them firing. And they are at Earth. Fortunately for the Enterprise, the final shot of the Vengeance that snatches them out of warp speed occurs when they are only 200,000 km from their destination. So it didn't matter that they caught up because probably 0.000001second after the critical shot the computer would've come out of warp speed anyway. Its just such shit writing it takes me right out of the movie for a moment whilst I shake my head . Didn't have this issue with ST09.