Thank you. I seem to have trouble using rate as a concept, especially dividing by it :) But I think I get it when I add a virtual distance into what you are saying.

You are saying (force / area) / (1 / time). I add two distances that cancel out: (distance * force / area) / (distance * 1 / time) and get (energy / area) / speed, which is energy used per area and speed. I can feel that, and it seems to be what you are saying, right?