I am of the opinion that this varies widely from case to case, and is very subjective. "Extremely similar" can be not so crystal clear. Sometimes, two answers with the same content have a different way of discourse which puts them apart. I think there is merit in the opinion that "redundancy is not necessarily bad", particularly in mathematics. This is something to keep in mind when judging these situations.
That said, if you think the answers are quite similar, I think it can be politely pointed out in the comments something like "Your answer seems to be pretty similar to X's. Can you consider adding some new perspective?" or something like that. I've seen this done, with low backlash.
If the case seems bad enough and you feel that the addition of that answer is not useful at all, you can downvote to indicate that (it is the most straightforward motivation for a downvote, as indicated when you hover the mouse over it). And this seems to be effective: if the answerer is just fishing for points, he unconsciously realizes that his answer is not that useful, and a downvote may make the penny drop. If he is not fishing for points, he will try to improve or justify why his answer is useful, and you may change your perspective.
The time gap is also relevant, and the "grace period" dependent on the question. 10-15 minutes later can be too much or not that much, depending on the question. It is really a case-by-case situation in my opinion. But, to give an objective answer and a rule of thumb:
If the answers are extremely similar to the point that the new answer adds nothing of value, consider downvoting the answer.
If the answer is a blatant copy in a literal sense (word by word), then flagging it may be appropriate.