document.write( "Question 127714: A painter works on a job for 10 days and is then joined by her helper. Together they finish the job in 6 more days. Her helper could have done the job alone in 30 days. How long would it have taken the painter to do the job alone? \n" ); document.write( "

Algebra.Com's Answer #93557 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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A painter works on a job for 10 days and is then joined by her helper. Together they finish the job in 6 more days. Her helper could have done the job alone in 30 days. How long would it have taken the painter to do the job alone?
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\n" ); document.write( "Let x = time required by the painter to do the job alone
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\n" ); document.write( "Let the completed job = 1
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\n" ); document.write( "Think of of it this way. The painter has 10/x of the job completed when he's joined by the helper
\n" ); document.write( " $\"10%2Fx\"$ + $\"6%2Fx\"$ + $\"6%2F30\"$ = 1
\n" ); document.write( "same as:
\n" ); document.write( " $\"16%2Fx\"$ + $\"6%2F30\"$ = 1
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\n" ); document.write( "Multiply equation by 30x to get rid of the denominator
\n" ); document.write( "30x* $\"16%2Fx\"$ + 30x* $\"6%2F30\"$ = 30x(1)
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\n" ); document.write( "30(16) + 6x = 30x
\n" ); document.write( "480 + 6x = 30x
\n" ); document.write( "480 = 30x - 6x
\n" ); document.write( "480x = 24x
\n" ); document.write( "x = $\"480%2F24\"$
\n" ); document.write( "x = 20 days, painter by himself
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\n" ); document.write( "We can check that using the original equation
\n" ); document.write( " $\"10%2F20\"$ + $\"6%2F20\"$ + $\"6%2F30\"$ =
\n" ); document.write( " $\"5%2F10\"$ + $\"3%2F10\"$ + $\"2%2F10\"$ = 1 \n" ); document.write( "

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