document.write( "Question 177538: working together,Joseph and Beth can encode a document in 3 hours.Working alone,Beth can do the job 5 hours.How long does it take Joseph to do the
\n" ); document.write( "job working alone? \n" ); document.write( "
Algebra.Com's Answer #132545 by gonzo(654)\"\" \"About 
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let x = rate that joseph works at = number of units produced in one hour.
\n" ); document.write( "let y = rate that beth works at = number of units produced in one hour.
\n" ); document.write( "let 1 = number of units to be produced (the document)
\n" ); document.write( "rate * time = number of units produced
\n" ); document.write( "working together, beth and joseph can do the job in 3 hours.
\n" ); document.write( "(x + y) * 3 = 1
\n" ); document.write( "working alone, beth can do the job in 5 hours.
\n" ); document.write( "y * 5 = 1
\n" ); document.write( "solving for y, we get y = 1/5 = rate that beth works at meaning she can produce 1/5 of the document in one hour.
\n" ); document.write( "we can substitute 1/5 for y in the equation:
\n" ); document.write( "(x + y) * 3 = 1
\n" ); document.write( "that equation becomes:
\n" ); document.write( "(x + 1/5) * 3 = 1
\n" ); document.write( "remove parentheses to get:
\n" ); document.write( "3*x + 3/5 = 1
\n" ); document.write( "subtract 3/5 from both sides to get:
\n" ); document.write( "3*x = 2/5
\n" ); document.write( "divide both sides by 3 to get:
\n" ); document.write( "x = 2/15
\n" ); document.write( "that is the rate that joseph works at meaning joseph can produce 2/15 of the document in one hour.
\n" ); document.write( "let t = the time it takes for joseph to complete the document.
\n" ); document.write( "rate * time = units produced
\n" ); document.write( "2/15 * t = 1
\n" ); document.write( "t = 15/2 = 7.5
\n" ); document.write( "it would take joseph 7.5 hours to complete the job.
\n" ); document.write( "verify in the original equation:
\n" ); document.write( "(x + y) * 3 = 1
\n" ); document.write( "substitute 1/5 for y and 2/15 for x to get:
\n" ); document.write( "(2/15 + 1/5) * 3 = 1
\n" ); document.write( "1/5 is the same as 3/15
\n" ); document.write( "equation becomes:
\n" ); document.write( "(2/15 + 3/15) * 3 = 1
\n" ); document.write( "which becomes
\n" ); document.write( "5/15 * 3 = 1
\n" ); document.write( "which becomes:
\n" ); document.write( "1/3 * 3 = 1
\n" ); document.write( "which becomes:
\n" ); document.write( "1 = 1
\n" ); document.write( "equation is good.
\n" ); document.write( "your answer is:
\n" ); document.write( "joseph can complete the job in 7.5 hours working alone.\r
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