document.write( "Question 130738: Working with your cousin, you can refinish a table in 8 hours. Working alone, your cousin can complete the job in 12 hours. How long would it take you to refinish the table working alone? \n" ); document.write( "

Algebra.Com's Answer #95459 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let's find the hourly rate of work:
\n" ); document.write( "Y = you and C = your cousin.
\n" ); document.write( "The two of you can refinish the table in 8 hours, so you both can do 1/8 of th table in one hour. Write this as:
\n" ); document.write( " $\"%28Y%2BC%29%281%29+=+1%2F8\"$
\n" ); document.write( "Your cousin alone can refinish the table in 12 hours, so he/she can do 1/12 of the table in one hour. Write this as:
\n" ); document.write( " $\"C%281%29+=+1%2F12\"$
\n" ); document.write( "Now, if you subtract these you can find out how much you can do in one hour.
\n" ); document.write( " $\"%28Y%2BC%29+-+C+=+1%2F8+-+1%2F12\"$ Of course, (Y+C)-C = Y, so...
\n" ); document.write( " $\"Y%281%29+=+1%2F8+-+1%2F12\"$
\n" ); document.write( " $\"Y%281%29+=+%283-2%29%2F24\"$
\n" ); document.write( " $\"Y%281%29+=+1%2F24\"$ So, in one hour, you can refinish 1/24 of the table. Multiply both sides by 24 to see how many hours it would take you to refinish the entire table.
\n" ); document.write( " $\"Y%2824%29%281%29+=+%2824%29%281%2F24%29\"$
\n" ); document.write( "

24 = 1}
\n" ); document.write( "So it would take you 24 hours to refinish the whole table. \n" ); document.write( "

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