Figuring out how to slow down a cassette tape that is playing too fast is simple, thanks to items you probably already have lying around.
Before you can fix the speed of a cassette tape, you have to make sure this is a fixable issue. Since cassette tapes are an outdated format for playing and recording, the speed needs to be the only problem in order for it to be remedied.
Locate a Walkman or other portable tape player that contains a typical headphone connection, as well as a cord that has a 2 1/2mm (headphone style) connection on each end.
Plug one end of the cord into the Walkman, and the other end into the line in jack found on your computer. DO NOT plug the cord into your microphone jack unless there is no other option. The microphone jack will tend to over-modulate and distort the sound.
Using a standard sound editing program, such as the freely downloadable Audacity, press record. After the recording has started, press play on the Walkman. When your song has played completely, stop recording and save your file.
Use the sound editing features to change the speed of your recording.
Another option is to purchase a recording system such as the VersaCorder manufactured by C.Crane company. This will allow you to play cassette tapes at 1/4 speed and, in some instances, other varying speeds.
Make sure tapes are clean and in good use. Old, damaged tapes will not play properly and/or respond to sound editing. As with any recording and editing, be observant of copyright laws.
Don't spend a fortune on playback systems you do not need and/or have the ability to operate. There are services available in many cities that will convert cassette tapes and edit speeds for you if this project becomes too arduous.