A small block of mass $m$ sits on a long board of mass $2m$. The board rests on a horizontal floor. The coefficient of kinetic friction between the block and the board is $\mu$, and the coefficient of kinetic friction between the board and the floor is $\mu/2$. Assume the coefficients of static friction are equal to their kinetic counterparts. At $t=0$, the block is given an initial velocity $v_0$ to the right, and the board is simultaneously given an initial velocity $v_0$ to the left. What is the total distance the board travels relative to the floor before coming to a permanent halt? Assume the board is long enough that the block never falls off.