This is a solution
20 on the hard interview questions node
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Start by lighting both ends of one rope and only one end of the second rope. When the first rope is finished burning (i.e., after a half an hour), light the other end of the second rope. At this point, the second rope is halfway burned, so it will take another 15 minutes to burn the second half with both ends lit. When the second rope is done burning, 45 minutes has elapsed.