Usually when two co-workers have a problem, then they will just hate each other and try to be better than the other. You can't say this because it is the wrong way to handle it. I would probably not deal with the problem and hate the other person, but that is not what I would say in an interview. You can mention that you believe having to deal with a problem with a co-worker is difficult because competitiveness comes into factor. Along with this statement, follow up with how you would try to look beyond that to make your relationship better.
This is showing answers by using scenarios. It is a solid answer but if you disagree, feel free to think of a good scenario that will fit you better.
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