Why don't interfering radio stations both play at the same time?
Your mention of the frequency (97.5 MHz) tells us this is an FM receiver.  (AM will behave differently, as will other modulation schemes).

Because FM is encoded by modulating the signal frequency, anything to do with AM is undesirable.  To deal with this, most receivers over-amplify the signal until it becomes larger than the later stages can pass.  The signal then "clips" to the voltage of that amplifier.  This stage is called a "limiter"--it limits the amplitude to some fixed value.  In theory, any signal weaker than that drops out and just becomes noise, and any signal stronger than that has a very nice fixed level that the FM detector can handle without having to worry about amplitude variations.

The amplifier-limiter stages create a phenomenon called "capture", where the strong signal tends to eliminate the weaker one.  This is why you hear only one station.  

If the signals were very close in strength, you would indeed hear them "mixing together", but that only happens for a fraction of a second as the signal levels rapidly change (presumably, you are in a vehicle), so you normally don't hear that.