Does "non-uniform rate" mean there may be a difference in the rate of each rope compared to the other? Or that the inches/minute rate of a single rope varies along its own length?

They both burn in an hour right? So they can differ one to the other. It must vary along each rope but end up taking hour.

Not specifically stated that they are the same length though, implied by the photo but that could be a ruse.

We don't know the length (L

_{1} or L

_{2})of either rope, we don't know the burn rate (dL/dt) of either rope, we don't know if dL/dt is a constant for either rope, we only know that for each rope the total time (t) = 60 minutes. I think the question is implying something that makes one of those variable known, or known relative to one of the other variables. I suspect the answer has something to do with connecting the ropes or looping them together in a creative manner exploiting that relationship.