When I fill up the gas tank on my truck, the gauge reads full and continues to read full for many miles (100 or 150 miles). After many miles, the gauge begins to slowly drop as additional miles are driven. If it drive it to 1/2 tank according to the gauge, I had better get gas because my tank is empty at this point. I know, I have run out with the gauge still reading 1/2 tank.

How can I tell where the problem lies?