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2021 JMPSC Sprint Problems/Problem 9

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.

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