document.write( "Question 990269: Working together, Sarah and Heidi can clean the garage in 6 hours. If they work alone, it takes Heidi 9 hours longer than it takes Sarah. How long would it take Heidi to clean the garage alone?
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Algebra.Com's Answer #610300 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Add their rates of cleaning to get rate
\n" ); document.write( "working together
\n" ); document.write( "[ 1 garage cleaned ] / [ t hrs ] = Sarah's rate
\n" ); document.write( "[ 1 garage cleaned ] / [ t + 9 hrs ] = Heidi's rate
\n" ); document.write( "[ 1 garage cleaned ] / [ 6 hrs ] = their rate working together
\n" ); document.write( "-------------------------
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28+t%2B9+%29+=+1%2F6+\"$
\n" ); document.write( "Multiply both sides by $\"+6t%2A%28+t%2B9%29+\"$
\n" ); document.write( " $\"+6%2A%28+t+%2B+9+%29+%2B+6t+=+t%2A%28+t%2B+9+%29+\"$
\n" ); document.write( " $\"+6t+%2B+54+%2B+6t+=+t%5E2+%2B+9t+\"$
\n" ); document.write( " $\"+12t+%2B+54+=+t%5E2+%2B+9t+\"$
\n" ); document.write( " $\"+t%5E2+-+3t+-+54+=+0+\"$
\n" ); document.write( "I notice that $\"+6%2A9+=+54+\"$
\n" ); document.write( "and $\"+6+-+9+=+-3+\"$ , so
\n" ); document.write( " $\"+%28+t+-+9+%29%2A%28+t+%2B+6+%29+=+0+\"$
\n" ); document.write( " $\"+t+=+9+\"$ ( can't have $\"+t+=+-6+\"$ , time can't be negative )
\n" ); document.write( "and
\n" ); document.write( " $\"+t+%2B+9+=+18+\"$
\n" ); document.write( "It will take Heidi 18 hrs to clean garage working alone
\n" ); document.write( "-----------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28+t%2B9+%29+=+1%2F6+\"$
\n" ); document.write( " $\"+1%2F9+%2B+1%2F18+=+1%2F6+\"$
\n" ); document.write( " $\"+2%2F18+%2B+1%2F18+=+3%2F18+\"$
\n" ); document.write( " $\"+3%2F18+=+3%2F18+\"$
\n" ); document.write( "OK
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