Ensure the engine has been cut off and that the mower is parked on a level surface. Allow the engine several minutes to cool before attempting to operate on it. Open the front hood over the engine to begin working on the throttle cable.
The throttle cable of the Sears 25 HP engine runs into and connects to the throttle arm on the engine's side. Take a pair of pliers and remove the housing over the throttle cable. Utilize a Phillips screwdriver to remove the lock screws located on the throttle arm's handle. This will allow you to disconnect the throttle cable from the engine. Dispose of the throttle cable.
Feed a new throttle cable through the housing. Ensure it is kept taut as you work it through the housing. Insert the new cable into the throttle arm's handle and secure it by inserting the removed arm handle screw with your Phillips screwdriver.
Test the engine. If the racing continues or if the engine fails, turn the engine off and revisit the throttle cable. Remove the arm handle screw with your screwdriver once more, and either feed more of the throttle cable into the housing or pull a bit out. Test different alterations in this manner until the mower's engine quits racing. Adjusting the throttle cable within the housing appropriately is key, so do not hesitate to revisit the throttle cable's positioning multiple times. Ensure that the cable is secured into the throttle arm handle before each engine test.