How can a 242 pound 61-year-old woman burn calories in 30 minutes?

You burn calories all the time, merely by staying alive. If you want to burn more calories, simply get your heart rate up. For your age and weight getting it to around or slightly below 120 is probably a good aimpoint.(other medical issues allowing) A stationary bike is good, walking is good if your legs can take it. Swimming is OK, but is unlikely to allow you such a pulse increase. 30 minutes is better than nothing, but if you want to cut weight you should try to keep it up longer. For 30-45 minutes you'll be able to keep going on just what's in your system, but if you push it beyond that you'll begin using up the energy that's stored in your fat as well.