document.write( "Question 1008104: Hannah and Lindsay clean an office. Hannah can clean the office alone in 3 hours. While Lindsay can in 2 hours. HOw long will it take them if they work together? \n" ); document.write( "

Algebra.Com's Answer #623860 by cparks1000000(5) $\"\"$ $\"About$

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Let $\"x\"$ be the amount of office space that Hanna can clean in 1 hour and $\"y\"$ be the amount of office space that Lindsay can clean in 1 hour. Let $\"A\"$ be the surface area of the room. Then $\"+2x+=+A+\"$ and $\"+3y+=+A+\"$ . Then let $\"t\"$ be the time it takes Hanna and Lindsay too clean the room together. Then $\"+t%28x%2By%29+=+A+\"$ .\r
\n" ); document.write( "\n" ); document.write( "Finally we solve for $\"x\"$ and $\"y\"$ in the equations not involving $\"t\"$ then plug into the third equation to get:
\n" ); document.write( " $\"+t%28+A%2F2+%2B+A%2F3+%29=+A\"$ \r
\n" ); document.write( "\n" ); document.write( "Then multiply through by $\"6%2FA\"$ to yield:
\n" ); document.write( " $\"t%28+3+%2B+2+%29+=+6\"$ \r
\n" ); document.write( "\n" ); document.write( "Thus the time it takes for them to clean the room together is 1.2 hours which is 1 hour and 12 minutes. \n" ); document.write( "

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