In this paper we consider the minimizing total weightedcompletion time in preemptive equal job length schedulingproblem on a single machine. We propose a polynomialtime algorithm that solves the problem. Before this paperthe problem were known to be open (see PhilippeBaptiste's web-resource http://www.lix.polytechnique.fr/~durr/OpenProblems/1 rj pmtn pjp sumWjCj/).