How long does my 20 lb propane tank last?

The answer to this question depends on which of your appliances  are using propane. Generally, an RV has a  refrigerator, water heater, furnace, stove and oven that use propane. By far the biggest gas hog is going to be the furnace followed by the hot water heater. If you are like me, you use your wheels to move to areas where you don't need to use your furnace. A lot of RV owners are now switching to catalytic heaters to cut down on fuel costs. Since I don't use my furnace when boondocking, I am only worried about eating and taking a hot shower if possible. My budget for propane is $15 which gets me a full 20 lb tank.

BTUs 
You will see your propane burners rated in BTUs which actually are BTUs per hour. So the first information you need to know is the BTUs for your water heater, refrigerator, and stove/oven.
When you see a propane stove or heater listed as 4000 BTUs, they mean 4000 BTUs per hour on high. Each 1 lb of propane is about 22,000 btus. So that means, you could run that burner on high for about 5 and 1/2 hours. If you turn on that 9000 btu hot water heater, you can expect to use a lb of propane about every 2 and a half hours. However, that water heater burner doesn't stay on high once it heats all the water because it takes less heat to keep water hot than to heat it up.

20 lb propane tank
Propane Gas produces the following:

1 gallon of Propane ~= 4.23 lbs ~= 91500 BTUs

1 lb of Propane ~=21630 BTUs

and a 20 lb tank of propane x 21630 BTU/lb ~= 432600 BTUs . So you have a total of  ~=432,600 BTUs to burn.

The refrigerator
So, let's  start with the refrigerator. The first thing is that it needs to be the right size to minimize the propane it uses. There are a lot of items kept in the refrigerator that don't really need refrigeration so this means you don't really need all that space. If you already have your refrigerator, look for its BTU rating. Refrigerators don't run all the time, so take that number and multiply it by .75. A 650BTU refrigerator will use 650*.75 or ~=488 BTUs per hour or 11700 per day. This means each day you run the refrigerator, it only uses a little over half a pound of propane.

The hot water heater
Since it takes so much propane to run the hot water heater, this is a trick that I use. It takes somewhere between 10-15 minutes to heat the water up to warm shower level. So set your kitchen timer for 15 minutes. This time can be adjusted to less in warmer weather. When the timer sounds,  shut off the heater and go take your shower. The water is just the right temperature, so just use the hot water tap full blast. Before you start, turn on the bathroom tap and drain the first couple of quarts into a container to use for doing dishes. This gets rid of the cold water left in the line. Don't forget to take that Navy shower. If the water heater is well insulated, it will stay warm the rest of the day for hand washing and dish washing.

Now, let's do that calculation. Since you are now running it for 15 minutes a day,  you get 1/4 of 9000 BTUs.  That means only 2250BTUs a day. So that is almost 10 days worth per lb. Not bad.

Total propane for refrigerator and hot water
Take the 2250 BTUs per day for hot water and the 11700 BTUs for refrigeration and you get a total of  ~=14000 BTUs per day. In 30 days, you will use 30 * 14000 or 420000 BTUS. This is almost your entire 20 LB propane tank. That doesn't leave anything left for cooking but there are ways to cut down on propane usage. In the National forest, I almost always cook on a wood fire. A thermal cooker or pressure cooker will cut the use of propane by 60-70% plus I have my solar cooker. I stay in 14 day intervals, often I eat up my cold stuff the first week and then turn off the fridge to save propane. Just remember it does take some time to cool back down. I also have a solar water heater for taking showers on warm sunny days.