Do Alice and Bill do the same work climbing a mountain?

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Homework Statement



Alice and Bill, who happen to have the same mass, both want to climb to the top of a mountain. Bill wants to take the steep path straight up, but Alice wants to take the path that gently winds around the mountain, even though it is 8 times longer than the steep path. They both eventually reach the top of the mountain, but Alice reaches the top in 1/3 the time that Bill takes using the steep route. How does the work that Alice did in climbing the mountain compare with the amount that Bill did?


Homework Equations


W= delta K


The Attempt at a Solution


They both do the same amount of work, correct? Since there KE at the bttom and top are the same?
 

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Answer depends a little bit on the context. If you are expected to treat it as an idealized case of work in gravitational filed then yes, amount of work depends only on the initial and final position, so if they start and stop at the same places amount of work is identical. But in reality it is not, as you do work even when walking horizontal surface.