Just for the sake of having an answer to address in general (not just your case) the issue of two answers saying the same thing ...
Don't post a duplicate answer long after the fact.
If someone posts an answer to a riddle and then weeks later someone else comes along and posts the same answer, that re-post will often be deleted even though it's technically an answer and maybe even a correct one. We don't need to clutter up the answer section with the same thing being posted every time someone else reads the post and figures out the solution.
But if two identical answers are posted near-simultaneously, that's usually OK.
This happens a lot on PSE: several people are reading a riddle at the same time, get the solution, and post their answers almost right on top of each other. Sometimes we've even had two answers with the exact same timestamp (down to the second), or three or four answers posted within a few seconds of each other. In these cases, there's no need to delete - sometimes the OP even decides to accept a slightly later answer, if it's somehow better than the first-posted answer.
You can delete your answer, if you want to. There's just no obligation to do so, and you won't be frowned upon for a second answer within seconds or minutes of the first.
There's no clear cutoff point for how close answers can be - just use common sense.
If one answer is posted a month after the other, it'll probably be deleted. If one answer is posted ten second after the other, that counts as near-simultaneous. I'm not even going to try nailing down a transition region. It also depends on the type of puzzle: a complicated and tricky grid-deduction puzzle takes much longer to solve than a four-line riddle, so it's more understandable in the former case if one answer is posted say 30 minutes after another even though both answerers were working simultaneously.