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Burning ropes

You have two ropes and some matches. Each rope, if lit at its end, will burn for 60 minutes. But the rate of burning is not regular, so cutting a rope in half doesn't result in a burn time of 30 minutes.
How can you use the ropes to time exactly 45 minutes?

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Tags: time
If you enjoyed this puzzle, check out Sunday Afternoon Maths I,
puzzles about time, or a random puzzle.

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