Answer Total Work Question: Understand Why Total Work is Zero with ΔPE

[Speedking96]

Below is the question:

My equation for Work Total is:

Delta PE = Wspring + Wgravity

However, the solution key says that the Wspring + Wgravity = 0

I fail to understand this, why is the total work zero when there is a change in potential energy?

 

[russ_watters]

[edit: better way to say it]
If you come up with both gravitational PE and another total PE, you end up with more energy than the spring put into the system. You're counting the GPE twice.