A floor cleaning system and a method of cleaning a floor are provided. The cleaning system includes a flat headed mop. The system also includes a frame and at least one compartment removably coupled to the frame. A wringing assembly is fluidly coupled to the at least one compartment, the wringing assembly comprising a fixed extractor element and at least one roller movable from a first position when the mop head is being inserted to a second position when the mop head is being withdrawn.