The January 2009 Problem of the Month

A large army that is 1 mile long is marching at 4 mph to their next conquest. A message needs to be sent from the rear to the front. So a messenger is sent to run to the front, deliver the message and run back to the rear.

The messenger runs at constant speed, and just so happens to return to the rear at the same time that the rear is now where the front was when the messenger first took off.

What was the messenger's speed?