A 5 mile long column of soldiers march in single file in a straight line at a constant speed. Dan, a mounted courier, leaves the rear of the column and rides for the front of the column at a constant speed. When he reaches the front he instantly reverses his ride to the rear of the column, going at the same speed. When he reaches the rear he discovers that he is at the spot where the front of the column was when he began his ride.
How far had Dan ridden?(correct to 3 decimal places)