If you light both ends of one rope, it will burn twice as fast.

Burn one rope from both ends and the other rope from only one end. it makes no difference which rope. Once the dual burning rope finally burns out, you will know 1/2 an hour has elapsed.

At this time you know that the second rope which you lit only on one end, has exactly 1/2 an hour remaining. If you now light this remaining rope on both ends, it will burn in 15 minutes. Thus totaling 45 minutes.

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