document.write( "Question 889057: Jerry and George are painting a house. Jerry can paint the house in 3 days less time than George. Together they can do the job in 6 days. How long will it take each of them if they work alone? Give your answer to the nearest tenth. \n" ); document.write( "

Algebra.Com's Answer #537879 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+d+\"$ = number of days George takes working alone
\n" ); document.write( "( 1 house ) / ( d days ) = George's rate
\n" ); document.write( "( 1 house ) / ( d-3 days ) = Jerry's rate
\n" ); document.write( "( 1 house ) / ( 6 days ) = rate working together
\n" ); document.write( "-------------------------------------------
\n" ); document.write( "Add their rates of working to get rate working together
\n" ); document.write( " $\"+1%2Fd+%2B+1%2F%28+d-3+%29+=+1%2F6+\"$
\n" ); document.write( "Multiply both sides by $\"+6%2Ad%2A%28+d-3+%29+\"$
\n" ); document.write( " $\"+6%2A%28+d-3+%29+%2B+6d+=+d%2A%28+d-3+%29+\"$
\n" ); document.write( " $\"+6d+-+18+%2B+6d+=+d%5E2+-+3d+\"$
\n" ); document.write( " $\"+d%5E2+-+15d+=+-18+\"$
\n" ); document.write( "Complete the square
\n" ); document.write( " $\"+d%5E2+-+15d+%2B+%28+15%2F2+%29%5E2+=+-72%2F4+%2B+%28+15%2F2+%29%5E2+\"$
\n" ); document.write( " $\"+d%5E2+-+15d+%2B+225%2F4+=+-72%2F4+%2B+225%2F4+\"$
\n" ); document.write( " $\"+%28+d+-+15%2F2+%29%5E2+=+153%2F4+\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"+d+-+15%2F2+=+sqrt%28+153+%29+%2F+2+\"$
\n" ); document.write( " $\"+d+=+%28+15+%2B+sqrt%28153%29+%29+%2F+2+\"$
\n" ); document.write( " $\"+d+=+%28+15+%2B+12.37+%29+%2F+2+\"$
\n" ); document.write( " $\"+d+=+27.37%2F2+\"$
\n" ); document.write( " $\"+d+=+13.685+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+d-3+=+10.685+\"$
\n" ); document.write( "George takes 13.7 days working alone
\n" ); document.write( "Jerry takes 10.7 days working alone
\n" ); document.write( "-----------------------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2Fd+%2B+1%2F%28+d-3+%29+=+1%2F6+\"$
\n" ); document.write( " $\"+1%2F13.685+%2B+1%2F10.685+=+1%2F6+\"$
\n" ); document.write( " $\"+.07307+%2B+.09359+=+.1667+\"$
\n" ); document.write( " $\"+.16666+=+.1667+\"$
\n" ); document.write( "OK
\n" ); document.write( "-------
\n" ); document.write( "Note that back when I took the square root of
\n" ); document.write( " $\"+153+\"$ , I could have used the negative square root,
\n" ); document.write( "but that would have resulted in each one working alone
\n" ); document.write( "doing the house faster than working together which
\n" ); document.write( "is impossible\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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