A turkey that's been marinating in a brine does actually cook a little faster. Because it contains more moisture, it cooks faster than if it had not been brined. I typically cook mine for about 2 1/2 to 3 hours, however this time could fluctuate a little depending on your oven. To ensure yours is cooked to perfection, check the temperature ever so often with a meat thermometer (insert it in the thickest part of the thigh). It will be cooked through when the temperature reaches 180°F.