Guys i need your i can't seem to really remember since i was absent the day my teacher taught this. can you guys me! ? is she correct? and why? i will make the brainliest if you answer both questions correctly

I do not believe that she is correct because I think that the same amount of work is done just at different paces, as in pushing the barrel up the ramp takes more time but less work per second whereas lifting the barrel takes a lot of work in a small amount of time, it's like imagine pushing a 10 pound medicine ball up a ramp in comparison to lifting it up, one takes longer than the other and the force that is being applied is lower but the work done will be the same in the end, this is also assuming you are excluding friction

As the height is same and potential energy depends on the height of ramp !!
as; PE = mgh

So work done will be same as she rolls or lift !!