Why does my water pressure drop after using my water hose for a few minutes?

The part that jumped out at me is this: "4" well with a submerged pump and a pressure tank in the garage."

How big is your pressure tank? My guess is that the greater water draw of a 1/2 or 5/8 inch hose can drain the tank in 15 minutes. The washer or shower has a much lower flow rate in gallons per minute used than a hose.

When the pressure is low from the hose, do you also get low pressure inside the house?

I would believe the pump isn't keeping up with demand and the pressure tank is supplementing it for the first 15 minutes.

Where I live the pump can run at full steam and the pressure tank is used for reducing the number of times the pump turns on and off.

Test - Turn off the pump attach a hose closest to the pump and drain the water tank. Leaving the hose open, turn on the pump. How is the water volume and pressure?

If the pressure is not that good after the test, then the pump itself doesn't put out the flow you need. At that point you could get a bigger tank to extend your 15 minutes.

@TNT is close, but it is likely that the well itself isn't keeping up with demand (low yield).

The well itself acts as a reservoir, and has water flowing into it from sand and fractures in the rock around it is drilled through. When the pump is off, the well will fill up a certain amount, after which point it will turn off. This is point is called the static head of the well.

The water will flow at a certain rate (which may vary depending on season, and where the water is actually coming from), and so that's the maximum flow rate you will get from your well. The flow rate can also change a bit depending on the amount of water already in the well: sometimes when the level is below a fracture, more water will come in, but when it's above, it won't contribute much.

Your pump itself will also have a maximum flow rate, which depends on the size of pump, motor, head (amount of water above the pump), depth (from the pump to pressure tank) and total distance of pipe. If your well doesn't produce at least this much water, you will be starving the pump for water and running out.

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When you first open the tap, the water will come from the pressure tank. As soon as the pressure drops to the cut-in pressure (usually ~40-50psi), the pump turns on and fills the tank up to ~60-70psi. When that happens, it's using water that is sitting in the well. If your well produces less water than your pump, eventually your pump will catch up and now be running dry, or very close to it.

In your situation, it sounds like your well yield is just slightly less than the pump can do, and so the pump is using up the reserve in the well, and then while the pressure drops it's on the edge of running dry (which can be very hard on the pump, btw).

You can buy a PRV, pressure reducing valve, from a hardware store to drop your pressure down. The problem with reducing it the way that you are is if the output is reduced the RO unit will get full pressure. I would go and look for a PRV if you want to reduce the pressure, I think that they are less than $10. It works on the same principle as the regulators for air compressors.

It appears that you've resolved the problem, but one thing to consider when troubleshooting issues with pressure tanks is the air-space at the top of the pump. Usually there's a tire-inflation valve somewhere near the top of the tank. Connect a bicycle pump to that and pump a bit more air in. The air space acts like a spring, maintaining the pressure. More air is equivalent to a bigger spring.

I had the same problem. We purchased an old cottage with an existing drilled well from the 1980's with a pump that was replaced in 2004. We renovated the cottage and added 2,200 sq ft to the house. All of the interior plumbing is new, but the well and pump were existing. After many hours of troubleshooting, I diagnosed the problem. Newer fixtures and appliances are designed to save water. On average, shower heads, faucets, toilets, dishwashers, etc are designed to use 2 gallons per minute or less. However, an outside hose at full throttle could use 5 gallons per minute, or more. A well has a "static" level, which is the level below grade the water naturally sits. In our well, the water is 8 feet from the top of the wellhead. The submersible pump is 200' down on a well that is 600' deep. We never saw a problem with water supply/demand inside the house, but after 30 minutes of watering with a garden hose sprinkler, the water pressure would drop to a trickle. Since we didn't drill the well, we have no idea what the output was when it was completed, but we had it checked recently and found it is only producing 2 gallons per minute. This is the root of our problem, and likely yours. Our pump is 200 feet down, but the static level is 8 feet. So if we are using water at a rate of 2 gallons per minute or less, the pump is only raising the water 8 feet. However, in the case of a lawn sprinkler using 5 gallons per minute, we are using 3 gallons per minute more than the well can produce. A 6" well whose pump is 200' down has a column of water that amounts to just under 300 gallons. As you use your sprinkler, you're using 3 gallons per minute more than the well can produce... which means in an hour and a half, your reserve is gone and your well pump is pushing water up 200'. This will lower your pressure as well as burn out your pump... and, you will only have 2 gallons p/min available, as you have gone through your surplus once you have drained the column of water. As to the solution... well... that's another matter. There is no way to increase the capacity of an existing well aside from fracking it or drilling deeper (both of which are risky, if you love the taste and quality of your water)... and expensive. The only work around would be to put a restrictor on your garden hoses (you can buy them on Amazon for $10). This would keep your garden hose from using more water than your well produces, so you wouldn't use up the reserve. I hope this helps!