You have two ropes and a lighter. Each rope takes exactly one hour to burn completely, but it does not burn evenly: one half can take much longer than the other. How can you measure exactly 45 minutes?
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The two ropes
You can't use strings as uniform time rulers: they burn unevenly. The key is to turn on different extremes to transform an hour into half an hour.
Hints
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- An irregular chord is not suitable for measuring half a chord.
- If enciendes a rope by the two extremos, it consume in 30 minutes.
- While one rope measures 30 minutes, the other can be prepared to measure the remaining 15.
Solution
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Answer: Light one rope at both ends and the other at one end. Call strings A and B. First string string A from both ends. At the same time, light rope B at one end only. Since A burns from both ends, it is consumed in 30 minutes, although its combustion is irregular. At that time, rope B has been burning at one end for 30 minutes. It has another 30 minutes of combustion left if it were to continue burning on only one side. Then you turn on the other end of B as well. By burning at both ends, those remaining 30 minutes are consumed in 15 minutes. This is how you measure: $$
30+15=45
$$ minutes.
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