document.write( "Question 988272: Christopher can paint the interior of his house in 28 hours. If he hires Cynthia to help him, they can do the same job together in 20 hours. If he lets Cynthia work alone, how long will it take her to paint the interior of his house? \n" ); document.write( "

Algebra.Com's Answer #608996 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Christopher can paint the interior of his house in 28 hours.
\n" ); document.write( " If he hires Cynthia to help him, they can do the same job together in 20 hours.
\n" ); document.write( " If he lets Cynthia work alone, how long will it take her to paint the interior of his house?
\n" ); document.write( ":
\n" ); document.write( "let c = time required by Cynthia working alone
\n" ); document.write( "let the completed job = 1
\n" ); document.write( ":
\n" ); document.write( "Each will do a fraction of the job, the two fractions add up to 1
\n" ); document.write( " $\"20%2F28\"$ + $\"20%2Fc\"$ = 1
\n" ); document.write( "multiply by 28c, get rid of the denominators
\n" ); document.write( "28c* $\"20%2F28\"$ + 28c* $\"20%2Fc\"$ = 28c
\n" ); document.write( "Cancel the denominators and we have
\n" ); document.write( "20c + 28(20) = 28c
\n" ); document.write( "560 = 28c - 20c
\n" ); document.write( "560 = 8c
\n" ); document.write( "c = 560/8
\n" ); document.write( "c = 70 hrs Cynthia working alone \n" ); document.write( "

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