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Riddle: Two Ropes Burning

You have two lengths of rope. Each rope has the property that if you light it on fire at one end, it will take exactly 60 minutes to burn to the other end. Note that the ropes will not burn at a consistent speed the entire time (for example, it's possible that the first 90% of a rope will burn in 1 minute, and the last 10% will take the additional 59 minutes to burn).

Given these two ropes and a matchbook, can you find a way to measure out exactly 45 minutes?

You may have to do two things at the same time...

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