Moving up the line:
where v_s is the speed of the Sergeant, v is the speed of the soldiers and T_1 is the time it takes for the Sergeant to get to the front of the line.
Likewise, going back down the line:
where T_2 is the time to get to the back of the line.
Solving the top equation for X, subbing this into the bottom equation, then solving for v_s/v gives me
So if we know the T's...