No, there is no way to tell until someone posts the answer, at which point (or soon after) you will get a bar at the top of your screen telling you that there are new answers, and asking if you want to load them.
However duplicate answers are not necessarily a bad thing. If someone comes along and posts the same answer hours or days later without expanding on it anymore than anyone else, that's just useless, but, in the first few minutes having duplicate answers helps to reinforce the answer.
If I'm leaving an answer and when I hit submit someone has beat me to it and write approximately the same thing, I just upvote their answer. I obviously believe it to be correct, so it deserves my vote for sure. If the same answer is posted by someone within a couple minutes too, I'll assume they were typing it already and haven't seen that it's already been answered. So if I see it I'll upvote it as well. The time an answer is posted doesn't affect the quality of the answer.
The point in me saying all that is that it doesn't hurt if someone is answering a question at the same time as you, and they beat you to it. You may still even get some upvotes from them, and others if it is a correct answer. If you want to compete with the first answer for votes and acceptance though you usually need to expand on it more.