GYM HElP

If you are looking to burn calories alone then doing a high intensity interval training cardio is the quickest way to burn a lot of calories in a small amount of time (20 mins max).

Low intensity steady state cardio is great at burning calories for fat loss as well but it takes longer - 40-60 minutes.

I personally would throw some weight lifting in and follow it up with HIIT cardio. You can build muscle (no, you won't get bulky) therefore increasing metabolism and you burn your calories with HIIT.

your weight loss will come from your diet, not your exercise. Since you should be eating back your exercise calories anyways (assuming you are using MFP's calculator) it shouldn't matter how many calories you burn since you eat them back.

That said, if I only had 45 minutes at the gym, here is what I would do. 10-15 minutes on a "full body" elliptical at higher level/resistance. By full body, I mean one of the ones that you use your arms too. Then, I would go do stronglifts 5x5 or some other full body/compound movement strength training routine for the remainder of the time.

I know you said, you want to focus on fat loss, but that doesn't mean no strength training. It will be time well spent to be training your muscles now. The logic behind what I recommended is that the 10-15 minutes of high resistance cardio will give your legs a pretty good pump as well as warming you up. It will also give you a few extra calories to eat and get your heart rate up quickly. Then the real focus is lifting heavy. Since you don't have much time, focus on movements that work lots of muscles at the same time - why I suggested stronglifts 5x5.

By keeping/building more muscle while you lose weight, your metabolism will stay up and will actually help you in the long term.

The first line is rubbish. Weight loss is just a negative energy balance. How you achieve that is pretty much dependent on how much energy you consume vs how much energy you expend, with the intermediary consideration of how your body stores and/or utilizes energy. That's a complicated subject and anything you might learn from here about nutrient partitioning is probably not going to help.

I spend roughly only 45 minutes in the gym as well. The time you spend exercising is irrelevant only if you apply some sort of progressive intensity within your workout window. If you can break a hard sweat by the 5 minute mark, and maintain a 160BPM heartrate for 45 minutes, you will not be complaining about not having enough time in the gym. How you achieve this kind of intensity is the beauty of exercise. Weight training can be very cardiovascular...I idle at about 155 BPM and I don't do any concentrated cardio (since my heartrate is already 155, my weight training and cardio serves the dual purpose of muscle gain, and fat loss, but not necessarily independent of each other). As to your question, you will plateau at some point. Maybe you'll be able to shed 20lb before you plateau, or maybe you'll plateau before you're at your goal. But just mathematics in itself will lead to the certainty that someday you will plateau. (same energy expenditure every day + same energy intake everyday = eventually your energy out will match your energy in....what we call "maintenance level")

The weight training will definitely be more efficient to weight loss in the long (very long) run, but few people on this website seem to be able to conjure up enough intensity to get to that point. (this is not these peoples' fault. like all things, those of us that have kind of fallen into a fitness lifestyle have started very young, so it's ingrained in our habits).