  We provide explicit formulaes for the first Kantorovich-Wasserstein distance
between stationary measures for iterated function scheme on the unit interval.
In particular, we consider two stationary measures with different
configurations of the weights associated to the same iterated function schemes
with disjoint images composed of: $k$ positive contractions or $2$ contractions
of different sign. We also study the case of two stationary measures associated
to different iterated function schemes.
