As others have said, a week to ten days. It should be long enough to mow after 6 weeks or so. It shouldn't be muddy though. You need to keep the surface moist but not wet. The area needs to be kept moist constantly until all the seeds sprout. If the seeds start to germinate and the area dries out they will die. Same with too much water, they don't get enough air and die. Unless you can be there to sprinkle every couple of hours , it's best to cover the area with straw to hold in moisture between waterings. After everything has sprouted and you have a good carpet of grass going you can start watering less frequently and more deeply. This helps the grass to grow deep roots and become more drought resistant.