Difference between revisions of "2021 JMPSC Sprint Problems/Problem 9"

(Solution)
 
Line 4: Line 4:
 
==Solution==
 
==Solution==
 
If the machine splits the metal into <math>6</math> pieces, then it made <math>5</math> cuts. Therefore, it makes <math>1</math> cut every <math>\frac{20}{5}=4</math> minutes. To split the metal into <math>20</math> pieces, the machine has to make <math>14</math> more cuts. This will take <math>14\cdot4=\boxed{56}</math> minutes.
 
If the machine splits the metal into <math>6</math> pieces, then it made <math>5</math> cuts. Therefore, it makes <math>1</math> cut every <math>\frac{20}{5}=4</math> minutes. To split the metal into <math>20</math> pieces, the machine has to make <math>14</math> more cuts. This will take <math>14\cdot4=\boxed{56}</math> minutes.
 +
 +
 +
 +
==See also==
 +
#[[2021 JMPSC Sprint Problems|Other 2021 JMPSC Sprint Problems]]
 +
#[[2021 JMPSC Sprint Answer Key|2021 JMPSC Sprint Answer Key]]
 +
#[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]]
 +
{{JMPSC Notice}}

Latest revision as of 17:14, 11 July 2021

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

Invalid username
Login to AoPS