Weeks, not months. Darn typos.
A question you did not ask that might help you. It takes about 25 hours for an egg to go through the hen's internal egg making factory. It can only be fertilized in the first few minutes of this journey. That means if a mating takes place on a Thursday, Thursday egg is not fertile. Friday's egg might or might not be, depending on timing. Don't count on it. Saturday's egg should be fertile.
A rooster does not necessarily mate with every hen available every day, that's why I said after a mating. But he doesn't have to. After the rooster hops off the hen stands up, fluffs up, and shakes. This shake gets the sperm into a special pouch near where the egg starts its internal journey. The sperm can remain viable in that pouch from 9 days to over three weeks. Most of us count on two weeks but it can vary. A lot of people use three weeks separation, it usually works. But four weeks is a bit safer.