A term coined to describe a long car ride in which teenagers or grown adults sit in silence. Often times, the music is turned up. Usually due to stress and irritation or simply not wanting to talk. Seldom times, it can be called when one is driving a "shitbox" and needs to figure out if "that sound" is coming from their car. Also similar to when parents call an "all quiet" car ride after their children bug them. Only driver and shotgun seats may call a "quiet car."
Emily and Kristy became bored with their friends conversations going on in the back seats. Therefore, Emily called a "quiet car time" as a polite excuse to turn the music up.