In this paper, we present a fully polynomial-time approximation schema (FPTAS) for some single machine problems, namely: - minimizing weighted total tardiness when all due dates are equal, - two cases of the total tardiness problem, - a special case of the generalized total tardiness problem and - maximizing weighted total tardiness. The FPTAS is obtained by converting a graphical algorithm and has the best running time among the known FPTAS for the problems, that is polynomial in n and 1/ε.