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" );
document.write( "\n" );
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 #41128 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=41128\">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" );
document.write( "------------<BR>\n" );
document.write( "Cindy DATA:<BR>\n" );
document.write( "Time = x hrs./job  ; Rate = 1/x job/hr.<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Eva DATA:<BR>\n" );
document.write( "Time = x+3 hrs/job  ; Rate = 1/(x+3) job/hr.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Together DATA:<BR>\n" );
document.write( "Rate = 1/x + 1/(x+3) = (2x+3)/(x^2+3x) job/hr\r<BR>\n" );
document.write( "\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "Cindy worked 8 hrs.<BR>\n" );
document.write( "Eva worked 6 hours.<BR>\n" );
document.write( "8*(cindy rate) + 6(eva rate)= 0.9 job<BR>\n" );
document.write( "8/x + 6/(x+3) = 9/10<BR>\n" );
document.write( "8(x+3)10 + 6x(10)=9x(x+3)<BR>\n" );
document.write( "80x+240+60x = 9x^2+27x<BR>\n" );
document.write( "9x^2-113x-240=0<BR>\n" );
document.write( "x=[113+-sqrt(113^2-4*9*-240]/18<BR>\n" );
document.write( "x=[113+-sqrt21409]/18<BR>\n" );
document.write( "x=[113+146,3181]/18<BR>\n" );
document.write( "x=14.41 hrs<BR>\n" );
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document.write( "If x = 14.41 the \"working together rate\" is <BR>\n" );
document.write( "(2x+3)/(x^2+3x) job/hr = (31.81)/(14.41^2+3(14.41))=31.81/250.88 job/hr<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "Let z be the number of hours required to \"finish the job\" <BR>\n" );
document.write( "(finish the job means do 0.1 of it).<BR>\n" );
document.write( "So, (31.81/250.88) z = 0.1<BR>\n" );
document.write( "z=0.788 hr<BR>\n" );
document.write( "z=0.788(60)=47.32 minutes (time required for them to finish the job together)<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );