document.write( "Question 315892: Three workers are named X ,Y,and Z. Suppose that together X and Y and can do a job in 4 hours, X and Z can do it in 6 hours, and X,Y and Z can do the job in 3 hours. How many hours will Y alone need to do the job?\r
\n" ); document.write( "\n" ); document.write( "A) 6hrs B) 8hrs C) 10 hrs D) 12 hrs \n" ); document.write( "
Algebra.Com's Answer #225994 by Earlsdon(6294)\"\" \"About 
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Let's first find the hourly rate of each group:
\n" ); document.write( "If X+Y can do the job in 4 hours, then they can do \"1%2F4\" of the job in 1 hour.
\n" ); document.write( "If X+Z can do the job in 6 hours, then they can do \"1%2F6\" of the job in 1 hour.
\n" ); document.write( "If X+Y+Z can do the job in 3 hours, then they can do \"1%2F3\" of the job in 1 hour.
\n" ); document.write( "These can be expressed as:
\n" ); document.write( "1) \"X%2BY+=+1%2F4\"
\n" ); document.write( "2) \"X%2BZ+=+1%2F6\"
\n" ); document.write( "3) \"X%2BY%2BZ+=+1%2F3\"
\n" ); document.write( "Express the first 2 equations in terms of X.
\n" ); document.write( "1a) \"Y+=+%281%2F4%29-X\"
\n" ); document.write( "2a) \"Z+=+%281%2F6%29-x\" Now substitute these for Y and Z in equation 3) to get:
\n" ); document.write( "3a) \"X%2B%28%281%2F4%29-X%29%2B%28%281%2F6%29-X%29+=+1%2F3\" Simplify and solve for X.
\n" ); document.write( "\"X+=+1%2F12\"
\n" ); document.write( "To find the hourly rate of Y, subtract \"X+=+1%2F12\" from equation 1).
\n" ); document.write( "\"X%2BY+=+1%2F4\"-\"X+=+1%2F12\"
\n" ); document.write( "-------------------
\n" ); document.write( "\"Y+=+1%2F6\" This is the hourly rate of Y, so it will take Y 6 hours to complete the job. \n" ); document.write( "
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