Working out is definitely harder mentally than physically. I'm down. No matter how bad you feel just do it. Once you get used to working out everyday you start to love the way it makes you feel. You just feel better after a hard workout. I don't have a ton of free time either. If you run as much as you can in an hour, keeping that heart rate high you will burn a ton of calories and feel great afterwards.
I want to add this you may think you can't run too out of shape joint problems etc. This is hard to accept you might just be mentally weak its hard to overcome but if you can you will be amazed at what you can do. Now if physically you can't run that long biking is way easier on the joints. Biking can be a extremely high intensity work out you have to push yourself mentally though.
When you 1st start exercising you will be super sore for at least 4 days but just push yourself exercise everyday even when your sore. You will stop getting sore if you stick to it.
I will say there are easier ways to get in shape I try to toughen my mind and body at same time. So this may be a bit too brutal for some people. It works though. I went from a chunky kid to pretty good athlete to chunky and back to athlete and this is how I was taught and its worked extremely fast for me.