While watching some planes fly overhead the other day, I began to wonder to myself. Could you theoretically approximate an aircrafts speed by the length of it's contrail?

Lets say there is a very low temperature, say around -50 to -60, and about 50% relative humidity. This producing a contrail that dissipates some distance behind the plane. Now, lets say there are two different planes flying in the same "perfect world" atmosphere, remember this is all theoretical. One flying at X speed and the other at Y.

Would one be able to guess how much faster one is traveling then another? Also if you knew the actual values for the temperature and humidity, could you create a formula to approximate the planes speed?

Cal