  Suppose we are given the free product $V$ of a finite family of finite or
countable sets $(V_i)_{i\in\mathcal{I}}$ and probability measures on each
$V_i$, which govern random walks on it. We consider a transient random walk on
the free product arising naturally from the random walks on the $V_i$. We prove
the existence of the rate of escape with respect to the block length, that is,
the speed, at which the random walk escapes to infinity, and furthermore we
compute formulas for it. For this purpose, we present three different
techniques providing three different, equivalent formulas.
