This question was tested by William Dement by asking subjects to record information about their dreams and comparing that with REM time.  With [these experiments][1], Dement concluded that time in dreams is nearly identical to time in waking life.

More [recent research][2] by Matthew Wilson focusing on memory consolidation in dreams adds an important detail to this however.  Dream sequences are often disjointed, on a faster time-scale, and not always sequential with respect to the events they reflect.

Think of it this way: If you watch a movie with your VCR set to fast-forward, then the time in the movie is faster than real-time, but you are nonetheless aware that you have been watching for a shorter period of time.  The same appears to be true of dreams: Dreams may play in fast-forward, but dreamers are nonetheless aware of the actual passage of time.


  [1]: http://indianapublicmedia.org/amomentofscience/time-passes-dreams/
  [2]: http://en.wikipedia.org/wiki/Hippocampal_replay