You should read the selfish gene. He has a chapter on this question.
The answer is that the time period depends upon the longevity (in generations) of the piece of DNA that you take as your “basic unit of selection”; the gene isn’t a precisely defined concept, rather Darwinian theory is parametric over the length of the basic unit of selection. In this case, it doesn’t really matter.
You should read the selfish gene. He has a chapter on this question.
The answer is that the time period depends upon the longevity (in generations) of the piece of DNA that you take as your “basic unit of selection”; the gene isn’t a precisely defined concept, rather Darwinian theory is parametric over the length of the basic unit of selection. In this case, it doesn’t really matter.