I'm not sure for the mp3 player...
but for getting it to work in the car I've found tape adapters aren't all that brilliant - they're quite hissy.
I used to use a radio adapter - you plug it into the cigarette lighter (for power) and into the headphone jack and tune the radio to 88.1Mhz and it comes through okay.
Ideally you want a stereo with an auxillary input, but these are relatively rare and/or expensive.
Jon