document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200899>Question 200899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ann and betty work together and complete a sales report in 4 hr. It would take Betty 6 hr longer, working alone to do the job than it would Ann.  How long would it take each of them to do the job working alone. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151130 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=151130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=amount of time it takes Ann working alone<BR>\n" );
document.write( "Then Ann works at the rate of 1/x of the report per hour<BR>\n" );
document.write( "Let (x+6)= amount of time it takes Betty working alone<BR>\n" );
document.write( "Then Betty works at the rate of 1/(x+6) of the report per hour\r<BR>\n" );
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document.write( "Now we are told that Ann and Betty can do the report working together in 4 hours. So Ann and Betty together works at the rate of 1/4 of the report per hour<BR>\n" );
document.write( "So we have:<BR>\n" );
document.write( "1/x + 1/(x+6)= 1/4 Multiply each term by 4x(x+6)<BR>\n" );
document.write( "4(x+6)+4x=x(x+6)  get rid of parens<BR>\n" );
document.write( "4x+24+4x=x^2+6x subtract x^2 and also 6x from each side<BR>\n" );
document.write( "4x+24+4x-x^2-6x=x^2+6x-x^2-6x  collect like terms<BR>\n" );
document.write( "-x^2+2x+24=0  multiply each term by -1<BR>\n" );
document.write( "x^2-2x-24=0-------------------quadratic in standard form and it can be factored<BR>\n" );
document.write( "(x-6)(x+4)=0<BR>\n" );
document.write( "x=6 and<BR>\n" );
document.write( "x=-4  disregard the negative value for x time in this problem is positive\r<BR>\n" );
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document.write( "x=6 hrs----amount of time it takes Ann working alone<BR>\n" );
document.write( "x+6=6+6=12 hours amount of time it takes Betty working alone\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "1/6 + 1/12=1/4<BR>\n" );
document.write( "2/12 +1/12=1/4<BR>\n" );
document.write( "3/12=1/4<BR>\n" );
document.write( "1/4=1/4\r<BR>\n" );
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document.write( "Hope this helps---ptaylor </SPAN>\n" );
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