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You have two pieces of rope and a lighter. Both pieces take 60 mins to burn but do not do so at an even rate. How can you measure when 45 mins are up?
Use the lighter as a measurement tool.
Fold one piece of rope, the length of it is 30min, fold it again the length is 15min. Lay the two bits of rope beside each other, burn one end of the longer one till it gets up to the shorter rope ( which will be a quarter of the size) then it will be 45min.
Actually the right answer is the following (because the rope does not burn uniformly, you cannot assume that a quarter of the size = a quarter of the duration): At time t=0, you lit up rope#1 by its 2 ends; and simultaneously you lit up rope#2 on one end. When rope#1 is fully consumed, 30 minutes will have passed, while rope#2 still has "30min of battery" (whatever which length was burnt): that is when you lit it up on its other end. 30/2 = 15. When rope#2 is finally consumed, a total of 45 minutes will have passed.
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