Pressure Cycling and Suspected Ruptured Line
Do you have a valve on the line from the well that is before the pressure tank?  If so, try this test.

Wait for the pump to run.  When turns off, shut the valve.  If the pressure tank holds, then the problem is on the well side of that valve.  If it doesn't then you have a big leak in the house plumbing somewhere.  (Imagine a broken line in a crawl space...)

Next check depends on the well hookup.

Most 20 year old houses have a pitless adapter.  Take the cap off the well. Often there is either a iron pipe even with the top of the casing.  Sometimes you will have to bring your own.  The top of the adapter is threaded, I think for 1" ID iron pipe.  You will want sufficient length of pipe to reach to the adapter and also a T connector and a couple of 6" nipples.  Put the T on one end of the pipe,  and the nipples in the side branches.  This prevents dropping the  whole pipe string down the well.

Before you start, but after you have taken the cover off do a cycle of the well.    Listen for water escaping around the pitless adapter.  Listen also for water from a cracked riser pipe.  You may be able to shine a flashlight down the well if you have a really bright one.

Turn off power to the well.

Screw the other end of the T into the pitless adapter.

There will also be a cable, usually about 3/32 or 1/8 This connects to the spring latch on the adapter. Often there is a safety rope too.  This is connected to the pump, and is used to rescue the pump if the riser pipe breaks.  Tie it to something solid.

Drill a hole in a a couple feet of 2x6, corresponding to the outer diameter of the riser pipe.  If you have no clue, drill holes of 1" 1.25" and 1.5"  Make the holes about 4-5 inches apart.  Not critical.  Run the board through a saw so that you now have half holes.  Cut a few scraps of wood.

Get help for this next step.  With the T bar pipe in the adapter, pull the latch, and pull up the pipe until the adapter is above the top of the well.  Put the two half boards on either side of the riser, and attach the scraps to the board with screws.  This will keep the pipe from dropping back into the well.

Open a tap in the house so that the pressure tank is below the cutin pressure. 

Now turn on the well.  Water should gush out of the adapter. As soon as you have good flow turn it off.  Should only be a few seconds.  Walkie talkies or cell phones make coordination easier.

Wait a while.  If your pump was cycling on a 30 second round, waiting a minute is lots.

Put your hand firmly over the  opening in the pitless adapter and turn the pump on again. If the water dropped in the well, there will be a slug of air in the riser pipe, you will feel it push against your hand before the water comes out.  1"line runs about 30 feet per gallon of water.  If your well is 100 feet to the top of the water, you will have about 3 seconds of air before the water hits your hand.  

If the water is immediate, (only a couple of inches of air in the top of the adapter) then the well is fine.

If there was a slug of air, then the foot valve in the well needs replacing. Or you have a big crack in the riser pipe.  Pull the entire riser string, replace the foot valve or the riser pipe and put everything back together.

If there was no slug of air, then you have a problem between the well and the pressure tank.  

Note that a failed gasket between the pitless adapter and its fitting in the casing would also account for this.  Replace the gasket just 'cause.

Edit:

Wow!  This actually helped someone.

If you replace a well pump, and you are using more than residential quantities of water (You have a tap running for more than an hour a day) give thought to a VFD drive pump.  VFD pumps use a 3 phase motor.  The controller box turns residential single phase into 3phase, and also adjusts the frequency.  This allows the pump to  start slowly, which is easier on the pump and on the well.  It can also be set to approach the cutoff pressure slowly, by reducing rpm.  The one I looked at for my well was rated at 10 gpm, but could self throttle down to 1 gpm.  This means that the pump doesn't cycle as often, which keeps the water level in the well bore more constant.  Rising and falling water levels tend to wash sand and mud out of the side walls.