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Lame, I know.(The ropes burn uneveningly and unequally. That is, half a rope won't necessarily burn in half an hour, and it won't necessarily be same amount of time as half of the other would take to burn - all you know is that the total time for one rope to burn is one hour.)
Yvtug ebcr 1 ng bar raq, naq ebcr 2 ng obgu raqf. Nsgre guvegl zvahgrf, ebcr 1 jvyy ohea bhg. Gura, yvtug gur bgure raq bs ebcr 2. Ebcr 2 oheaf bhg svsgrra zvahgrf yngre.
But even then: (rot13) Guvf nffhzrf gung Ebcr 1 ohearq svsgl creprag va gur gvzr vg gbbx ebcr 2 gb ohea. Vs ebcr 1 bayl ohearq bar dhnegre, gura vg jvyy gnxr gjragl-gjb naq n unys zvahgrf, abg svsgrra, nsgre yvtugvat gur bgure fvqr.
Anu, vg qbrfa'g nffhzr gung. Vs ebcr 1 gnxrf 1 ubhe gb ohea, naq lbh ohea vg sbe unys na ubhe, gura vg unf unys na ubhe yrsg bs ohea gvzr. Vg qbrfa'g znggre vs gur svefg unys ubhe gbbx hc 10%, 50% be 90% bs gur ebcr yratgu, vg jvyy fgvyy svavfu oheavat va nabgure unys ubhe.
It took me a while to realize that cutting it lengthwise was the whole problem.
If a part solution hadn't been given (tie the rope in a loop) then you might even be able to gnaw through the rope so you have it in two pieces - one to wrap around yourself as a harness so you can slide about as you work the rope down the tower. These solutions do assume that the diameter of the tower is consistent in both directions.
Although if it got thicker on the way down you might be able to loop slack into it higher up and then consume this as you descend.
http://www.paddling.net/sameboat/Images/knotrope.gif The image shows what I've now learned is called "laid rope"