Ok.. some quick ones. It almost sounds like a broken pipe, possibly under the foundation. Yes there is a way to locate it, but you probably do not have the tools.
With the water on.. running for about 1 day if checking for moisture near the foundation.
Are you on slab or raised floor (most newer houses are on slab)
How fast (cu feet/min or gal/min) is the leak?
About when was the construction of the house.
Is there any water appearing around the foundation, or is ground near an area of the foundation wetter than normal?
Hopefully none of the carpet nor walls(check near the bottom of the walls – where they meet the carpet) are getting wet.
Is the output side of the hot water heater always hot, even if someone has not taken a bath, done dishes, washed clothes for quite a while (hot water heater may be cycling more often than normal)
If it is under the slab, a person will have to locate the leak through sound. There is a tool for doing this. They will then have to pull up any carpet over the particular area followed by cutting/jack-hammering through the slab to get to the leak. They then cut out the bad segment followed by replacing the sand, moisture membrane, concrete and then finally sewing together any carpet that they need to.
