My odometer quite working and my speedometer shows my car going 10 mph faster than it actually is going. Would changing the speed sensor correct this problem?
Its possible. There is also a possibility that the cluster is broken.
If you have a manual speedometer, your magnate inside may be getting weak, and or the nylon gears may be letting go and showing wear. Take it to a good speedometer shop and they may be able to tell you. I had the same problem with my 69 Corvette, and a rebuild fixed everything.