If you work out 3 days a week and limit your calorie intake how long will it take to lose 20 pounds?

It depends on how many calories your body burns (this is your BMR, there are lots of sites that calculate it for you, google it) in a day vs. how many you eat. You need to burn 3,500 calories to lose one pound. If you burn an extra 500 calories a day, you'll lose 1 pound a week, so you'll lose 20 pounds in 2 months. It's okay to aim to lose 1-2 pounds a week... but any more than that is unhealthy and you'll pay for it in long run. Also, don't cut your calories below 1200 a day.