# Difference between revisions of "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.