+33661 Hmm. I've re-read the question more carefully.
It says to treat the runner as a point mass, m and so implicitly assumes that the force she applies to the mass comes from outside the mass. ie her leg muscles are outside of herself, though their mass is included within! In this case her (massless) muscles do indeed provide an upward force on her (massive) point body, and we can think of the force as being upward!
So, choose your preferred weirdness: pushing the Earth down or massless legs pushing a point body up!
I think the latter is a dangerous way of looking at this as it is may too easily lead to confusion in more complicated situations where there could be several internal forces that actually contribute nothing to the motion of the object in question (a point has no internal structure).
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+23252 Because she's moving upward ...
Her work must be expressed upward because she is moving upward against the force of gravity which is pulling her downward.
+118677 The velocity is upwards because she is moving upwards.
There is a gravitational force on her body that is downwards but she is countering that with a great force that is moving her upwards. So the force she is exerting is upwards and the net force is also upwards.
I think that is all correct. 
+33661 I don't think she is applying an upward force. She is applying a downward force on the Earth (through the stairs) and so is moving the Earth (and hence the stairs) downward, relative to herself!
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+118677 I am sorry for my false informations 315.
I think that you know by now that my physics is very shaky.
I wouldn't give you wrong info on purpose but you always need to be wary of my physics answers.
thanks for the correction Alan. 
+33661 The question is worded sloppily in my view. The runner does work using a downward force to move the Earth down by a certain distance, so the two negatives cancel each other out and the runner does some positive work!
Of course, that's a slightly weird way of looking at the situation, but if you are going to insist on careful use of signs in calculating the work (as the question does) then that's the way it should be done.
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+33661 Hmm. I've re-read the question more carefully.
It says to treat the runner as a point mass, m and so implicitly assumes that the force she applies to the mass comes from outside the mass. ie her leg muscles are outside of herself, though their mass is included within! In this case her (massless) muscles do indeed provide an upward force on her (massive) point body, and we can think of the force as being upward!
So, choose your preferred weirdness: pushing the Earth down or massless legs pushing a point body up!
I think the latter is a dangerous way of looking at this as it is may too easily lead to confusion in more complicated situations where there could be several internal forces that actually contribute nothing to the motion of the object in question (a point has no internal structure).
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