Okay, so the ideal gas law calculation is correct, that's good. The problem doesn't explicitly state whether the flask is sealed and vacuous, but I would assume that that is the intended meaning.
However, as I have stated, I think there is a problem with the question itself. My chemistry book (and wikipedia for that matter) says that "vapor pressure" is the same as "equilibrium vapor pressure". Can you corroborate this statement? If so, doesn't that mean that the answer to the problem is in fact 149 mm Hg because that is the equilibrium vapor pressure of water at 60 degrees C?