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2021 JMPSC Sprint Problems/Problem 9

Revision as of 16:14, 11 July 2021 by Samrocksnature (talk | contribs)
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Problem

A machine cuts a piece of metal at a constant rate. After leaving the machine alone for twenty minutes, the metal has been split into six pieces. How many more minutes will it take until there are twenty pieces?

Solution

If the machine splits the metal into $6$ pieces, then it made $5$ cuts. Therefore, it makes $1$ cut every $\frac{20}{5}=4$ minutes. To split the metal into $20$ pieces, the machine has to make $14$ more cuts. This will take $14\cdot4=\boxed{56}$ minutes.


See also

  1. Other 2021 JMPSC Sprint Problems
  2. 2021 JMPSC Sprint Answer Key
  3. All JMPSC Problems and Solutions

The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition. JMPSC.png

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