document.write( "Question 1036373: person A can finish a piece of work in 12hrs less than person B.If they work together 4/9 of the work is done in 5hrs.How long does it take them to do the work? \n" ); document.write( "

Algebra.Com's Answer #651030 by stanbon(75887) $\"\"$ $\"About$

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person A can finish a piece of work in 12hrs less than person B.If they work together 4/9 of the work is done in 5hrs.How long does it take them to do the work?
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\n" ); document.write( "B's time = x hrs/job ; B's rate 1/x job/hr
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\n" ); document.write( "A's time = x-12 hrs/job ; A's rate 1/(x-12) job/hr
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\n" ); document.write( "Together rate = (1/x) + 1/(x-12) = [x-12 + x]/[x(x-12)] = (2x-12)/(x^2-12x) job/hr
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\n" ); document.write( "Equation:
\n" ); document.write( "time*rate = work done
\n" ); document.write( "5[(2x-12)/(x^2-12x)] = 4/9
\n" ); document.write( "-------
\n" ); document.write( "45(2x-12) = 4x^2-48x
\n" ); document.write( "90x - 540 = 4x^2 - 48x
\n" ); document.write( "4x^2 - 138x + 540 = 0
\n" ); document.write( "x = 30 hrs (time B takes to do the job alone)
\n" ); document.write( "x-12 = 18 hrs (time A takes to do the job alone)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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