In this paper, we address the node repair problem of Reed-Solomon (RS) coded distributed storage systems. Specifically, to overcome the challenges of multiple-node failures of RS codes under the rack-aware storage model, we employ good polynomials to guide the placement of the conventional RS codes into racks and then propose a novel repair framework for the resultant rack-aware RS codes, which can transform its repair to that under the homogeneous storage model. As applications of our repair framework, firstly we present the repair scheme of multiple-node failures for some existing constructions, which only have non-trivial solutions for repairing a single-node failure before. Secondly, we deduce several new constructions of rack-aware RS codes supporting the repair of multiple-node failures within a single rack and across multiple racks respectively.