6 year old Toto Carlyle keeps running

I have a 6 year old Toto Carlyle and it keeps sending water into the overflow pipe. At times I even see water coming out of the refill tube. We replaced the assembly cap and all seems well. But about 2 hours later the water is spilling into the overflow pipe. If I wait a few more hours, that is when I notice the water coming out of the refill tube. Our water bill keeps getting more expensive because of this problem. Please help!!

The cap usually resolves that problem. Did you adjust the height of the fill valve? What is the water pressure in your house? You sure you got the float back on the little ears so it can move up and down freely?

But about 2 hours later the water is spilling into the overflow pipe.

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The cap will fix the fill valve,
But if the flapper is leaking and the tank is losing water, then the fill valve will turn itself back on to refill the tank.

First you have to make sure that the tank is not losing water.
If it takes two hours for the fill valve to turn back on, that would indicate a leaking Flapper