Special Relativity

A traveler stands on a platform watching a speeding train go by.  He sees a woman inside the train walking down the aisle toward the front of the train.  It appears that the woman is moving very quickly. 

At the same instant, a passenger in the train sees the same woman walking by his seat toward the front of the train.  To him it appears that she is moving slowly. 

Which observer do you think is correct?  Is she moving quickly or slowly?