A swimming pool is 12 feet wide, 30 feet long, and 10 feet deep, and the pool is initially 90% filled with water. A hose is placed in the pool, and water flows into the pool through the hose at a constant rate of one lb_m every 8 seconds, until the pool is completely filled. During this time, an inch of rain falls, and a 30 gallon rain barrel full of water is emptied into the pool. How long, from the moment the hose is turned on, does it take to fill the pool? Assume the density of water is constant at 62.3 lb_m/ft3.