You find yourself locked in a room which is filled with nothing but ropes of various
length and composition. All of these ropes have inconsistent compositions and densities,
even within themselves, but they all have one common property:
If you set a rope on fire from one end, it will take precisely one hour to
burn to the other end.
It is important to note that because the ropes are warped, with inconsistent
composition and density, they do not burn evenly. For example, if a rope has burned
half its length, that does NOT necessarily mean that it has burned for half an hour.
There is an exit to the room, with a lever to operate the door. In order to open
the door, you must first pull the lever and then the push it back into place
precisely 45 minutes later.
With nothing but a lighter and knowledge of the hour burning ropes, how can you
accurately time 45 minutes to open the door?