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?
Retrieve (2) ropes, we'll call them rope A and rope B.
Simultaneously light BOTH ends of rope A and ONE end of rope B on fire.
When rope A is completely burnt, 30 minutes have elapsed and rope B has "30 minutes worth" of rope left to burn. Light the other end of rope B on fire at this time.
Since rope B had "30 minutes worth" of rope left to burn and both ends are burning after the last step, rope B will be completely burnt in another 15 minutes.
The 15 minutes from the last step and the 30 minutes for the previous makes for 45 minutes, the exact time to solve the puzzle.