document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=59923>Question 59923</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073268620/algebrahomeworkh>Elementry and Intermediate algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I need a bit of help on this one....\r<BR>\n" );
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document.write( "It usually takes Eva 3 hours longer to do the monthly payroll than it takes Cindy. They start working on it together at 9.00 AM and at 5.00 PM they have 90% of it done. If Eva took s 2 hour lunch break while Cindy had none, then how much longer will it take for them to finish the payroll working together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41132 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=41132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It usually takes Eva 3 hours longer to do the monthly payroll than it takes Cindy. They start working on it together at 9.00 AM and at 5.00 PM they have 90% of it done. If Eva took s 2 hour lunch break while Cindy had none, then how much longer will it take for them to finish the payroll working together?<BR>\n" );
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document.write( "Start with what we know:<BR>\n" );
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document.write( "Together:<BR>\n" );
document.write( "Cindy worked from 9 til 5 w/o lunch so she worked 8 hrs to be 90% done<BR>\n" );
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document.write( "Eva took a 2 hr lunch break so she worked 6 hrs to be 90% done<BR>\n" );
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document.write( "Let the completed job = 1, then 90% of the job = .9<BR>\n" );
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document.write( "Let t = the amt of time required when Cindy works by herself<BR>\n" );
document.write( "Then (t+3) = amt of time required when Eva works by herself<BR>\n" );
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document.write( "An equation to get it 90% done<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ft+%2B+6%2F%28t%2B3%29 ALIGN=MIDDLE  ALT=\"8%2Ft+%2B+6%2F%28t%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .9<BR>\n" );
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document.write( "GEt rid of the denominators, mult eq by t(t+3):<BR>\n" );
document.write( "8(t+3) + 6t = .9(t(t+3)<BR>\n" );
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document.write( "8t + 24 + 6t = .9t^2 + 2.7t<BR>\n" );
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document.write( "0 = .9t^2 + 2.7t - 8t - 6t - 24<BR>\n" );
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document.write( "A quadratic equation, use the quadratic formula:<BR>\n" );
document.write( ".9t^2 - 11.3t - 24 = 0<BR>\n" );
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document.write( "The positive solution: t ~ 14.4 hrs for Cindy to complete the job by herself<BR>\n" );
document.write( "Then we know that it took 17.5 hr for Eva to do it by herself<BR>\n" );
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document.write( "They ask how much longer it will take to complete the job.<BR>\n" );
document.write( "Let x = the additional time required for them to complete the job:<BR>\n" );
document.write( "Let 1 = the completed job<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2Bx%29%2F14.4+%2B+%286%2Bx%29%2F17.4 ALIGN=MIDDLE  ALT=\"%288%2Bx%29%2F14.4+%2B+%286%2Bx%29%2F17.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "The common denominator would be 14.4*17.4 = 250.56, mult equation by that:<BR>\n" );
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document.write( "17.4(8+x) + 14.4(6+x) = 250.56<BR>\n" );
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document.write( "139.2 + 17.4x + 86.4 + 14.4x = 250.56<BR>\n" );
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document.write( "17.4x + 14.4x = 250.56 - 139.2 - 86.4<BR>\n" );
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document.write( "31.8x = 24.96<BR>\n" );
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document.write( "x = 24.96/31.8<BR>\n" );
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document.write( "x = .785 hrs to complete the job, that's about 47 minutes<BR>\n" );
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document.write( "To check it, using the time to complete the job together:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.785%2F14.4+%2B+6.785%2F17.4 ALIGN=MIDDLE  ALT=\"8.785%2F14.4+%2B+6.785%2F17.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( " .610 + .395 = 1.005 which is pretty close\r<BR>\n" );
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document.write( " </SPAN>\n" );
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