Work & Energy: When to Use PE vs KE?

[LexRunner]

I have been studying the Work and Energy chapter of physics and am currently confused on when to make work equal potential energy and when to make it equal to change in kinetic energy. Some of the problems have the work equal to change in KE and some have it equal to PE.
For example, why is work in this problem,
"Calculate the average power output necessary for a 55.8 kg person to run up a 12.0 m long hillside, which is inclined at 25.0° above the horizontal, in 3.00 s. Express your answer in horsepower"
set to equal PE rather than KE?

 

[Simon Bridge]

The total change in energy is going to be zero.
If the energy change of what you are looking at is not zero - then some energy was added or removed from it.
That is the work.

This could be a change in kinetic energy, in potential energy, or a bit of both.
At your level - either kinetic energy or potential energy will be changing. Just work out which one.

In your example - it implied by the wording that the kinetic energy has not changed ... the person is running at the same speed at the top of the hill as at the bottom. Thus the change in kinetic energy is zero - contributing nothing to the calculation.