Kipnis and Varadhan et al. proved that the tagged particle for non- nearest neighbour symmetric exclusion process on the one dimensional integer lattice has positive speed provided condition H-1holds and a strengthening of one part of condition H-1 also holds. We extend the result to a model in which only the tagged particle jumps either one or two steps, while all the others perform nearest neighbour jumps, assuming both condition H-1 and a variant of the additional condition used by Kipnis and Varadhan hold.