Burning Ropes 1
You have two ropes, each of which takes 1 hour to burn. But either rope has different densities at different points, so there is no guarantee of consistency in the time it takes different sections within the rope to burn. How do you use these two ropes to measure 45 minutes?
Answer
Light both ends of the first rope and one end of the second rope simultaneously. The first rope will be completely burned in 30 minutes (because lighting it from both ends halves its burn time). At the moment the first rope finishes burning (30 minutes have elapsed), light the other end of the second rope. The second rope, which would have taken 30 more minutes to burn from one end, will now burn in 15 minutes from both ends.
Hence, when the second rope is burned out, a total of \(30 + 15 = 45\) minutes will have passed.
Notes and comments
Comment 1: An important insight is that even though the rope burns unevenly, this does not change the fact that lighting it from both ends will take half the time. What changes from this assumption is that the meeting point need not be the center.