Burn the Ropes

You have two ropes and a lighter. Each of the ropes burns out in exactly 60 minutes, but not at a uniform rate – it is possible for example that half of a rope burns out in 40 minutes and the other half in just 20. How can you measure exactly 45 minutes using the ropes and the lighter?

First, you light up both ends of the first rope and one of the ends of the second rope. Exactly 30 minutes later the first rope will burn out completely and then you have to light up the other end of the second rope. It will take 15 more minutes for the second rope also to burn out completely, for a total of 30 + 15 = 45 minutes.

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  1. I do not think the logic here is valid. Assume the rope is half fast burning (20 minutes) and half slow burning (40 minutes). If lit from one end it will take 60 minutes to burn out. However if you light it at both ends, 20 minutes into the burn the fast end will be gone and that flame will start consuming the slow end. Which will now be burning from each end doubling its’ rate. So the rope would burn in 50 minutes with that ratio.

    1. Hi Daniel. After 20 minutes, the slow end would have burnt out completely and the slow end up would have burnt out halfway. Then, the slow end will need only 10 more minutes burning from both ends, so you get 20+10=30 minutes total.