document.write( "Question 1080277: One custodian cleans a suite of offices in 2 hours. When a second worker is asked to join the regular custodian, the job takes only 1 and one third hours. How long does it take the second worker to do the same job alone? \n" ); document.write( "

Algebra.Com's Answer #694451 by josmiceli(19441) $\"\"$ $\"About$

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1st custodian's rate of working:
\n" ); document.write( "[ 1 office cleaned ] / [ 2 hrs ]
\n" ); document.write( "Their rate working together:
\n" ); document.write( "[ 1 office cleaned ] / [ 4/3 hrs ]
\n" ); document.write( "Let $\"+t+\"$ = the second worker's time
\n" ); document.write( "in hrs to clean the office
\n" ); document.write( "-----------------------------------
\n" ); document.write( "Add their rates of working to get their
\n" ); document.write( "rate working together
\n" ); document.write( " $\"+1%2F2+%2B+1%2Ft+=+1%2F%28%284%2F3%29%29+\"$
\n" ); document.write( " $\"+1%2F2+%2B+1%2Ft+=+3%2F4+\"$
\n" ); document.write( "Multiply both sides by $\"+4t+\"$
\n" ); document.write( " $\"+2t+%2B+4+=+3t+\"$
\n" ); document.write( " $\"+t+=+4+\"$
\n" ); document.write( "The 2nd worker takes 4 hrs to do the job alone
\n" ); document.write( "---------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F2+%2B+1%2Ft+=+3%2F4+\"$
\n" ); document.write( " $\"+1%2F2+%2B+1%2F4+=+3%2F4+\"$
\n" ); document.write( " $\"+2%2F4+%2B+1%2F4+=+3%2F4+\"$
\n" ); document.write( " $\"+3%2F4+=+3%2F4+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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