It could take months. Its practically guaranteed she will stick for over a month if you dont do something. A hen builds up excess fat, especially the fat pad in the vent area. They live off this fat when they are broody. Thats why they can go so long without eating much while they are broody. Theyll lose a lot of weight while broody, but that is just excess fat until it runs out. Some will break from being broody then but some will just keep on going. Thats when it gets dangerous for them.
In my opinion, if a hen goes broody, you need to either give her fertile eggs to hatch, chicks to raise, or you need to break her. If you want fertile eggs let me know real soon and Ill get a half dozen in the mail to you. Im going to a wedding this weekend so they will need to be in the mail by Thursday. Ive still got your address. Or I can ship them the middle of next week.
If you decide to break her, you can read all kinds of ways; throw her off the nest (never worked for me) dunk her in cold water or make her sit on ice (never tried either). The way Ive always used and have always been successful is to put the broody hen in a raised cage with a wire bottom. Put food and water in there, even a roost if you want, but no bedding and nothing that looks like a nest. You want the air to blow on her bottom and cool her. Keep her in there for three full days and nights. If she heads back to her nest when you let her out, do it again, maybe for 4 days. Ive never had to do it a second time but some hens might be more stubborn than others.
My way to tell if a hen is really broody is that she stays on the nest for two consecutive nights instead of roosting in her normal place. Them going broody is caused by hormones. Ive had several act like they are going broody, even as far as spending one night on the nest, but never kick over into full broody mode.