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To find out how long it will take Stacy to paint the entire room, we need to figure out how long it takes her to paint 1/4 of the room and then multiply that by 4 to get the total time.
Stacy can paint 3/4 of the room in 3 hours.
So, Stacy can paint 1/4 of the room in 3/4 * 1/3 = 1/4 * 1/3 = 1/12 of the time it takes her to paint 3/4 of the room.
Therefore, it will take Stacy 3 * 12 = <<3*12=36>>36 hours to paint the entire room. Answer: \boxed{36}.