Wendy,
How old/big is your boa? Is it male or female? Where on Earth are you (hehehe)? Temperature changes are one of the most common causes of tropical snakes going off food. You seem unsure of when the snake last ate, did you just get it? Nevermind, I just reread your post - he likes B&W rats, so apparently he has eaten for you (or were you told this?). Does it eat live, f/k, or f/t? Has it shown any interest in the rats? What do you keep the snake in (enclosure), how do you heat it, what are the temps (warm side, cool side, hi/low, and room)? When was the last shed? Is it drinking? When was the last time it had a bowel movement? How often, and for how long, do you handle it? You said he now has a B&W rat...is there a live rat in with the snake?
Jeez, I ask a lot of questions, don't I? Now to answer yours (sort of): How long they stop eating depends on why they stopped, and how long it takes us to correct the problem. Yes, it is normal for snakes to stop eating - in a way - it is a natural response to stress, changing conditions, and illness.
My first guess is that with the arrival of colder weather, the cage temperatures have dropped a bit...but that is pending your response to my questions