document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=682905>Question 682905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Apprentice pastry chef Michael takes 9 hours longer than pastry chef Sofia to prepare enough cannoli shells for a wedding. Together, the two can complete the job in 20 hours. How long does it take each person 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 #423380 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=423380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sofia prepares enough shells in x hours<BR>\n" );
document.write( "Then Sophia works at the rate of 1/x of the needed shells per hoour<BR>\n" );
document.write( "Michael takes x+9 hours to make enough shells<BR>\n" );
document.write( "Then Michael works at the rate of 1/(x+9) of the needed shells per hour<BR>\n" );
document.write( "Together they work at the rate of 1/20 of the needed shells per hour,<BR>\n" );
document.write( "Soooooo:<BR>\n" );
document.write( "1/x + 1/(x+9) =1/20  multiply each term by 20x(x+9)<BR>\n" );
document.write( "20(x+9)+20x=x(x+9) get rid of parens<BR>\n" );
document.write( "20x+180+20x=x^2+9x  simplify<BR>\n" );
document.write( "x^2-31x-180=0 quadratic in standard form and it can be factored<BR>\n" );
document.write( "(x-36)(x+5)=0<BR>\n" );
document.write( "x=36 hours---- time it takes Sophia working alone<BR>\n" );
document.write( "x+9=36+9=45 hours ----time it takes Michael working alone<BR>\n" );
document.write( "Also <BR>\n" );
document.write( "x=-5---------------------no good --can't have negative numbers in this problem<BR>\n" );
document.write( "CK<BR>\n" );
document.write( "in 20 hours, Sophia does 20/36 of the needed shells<BR>\n" );
document.write( "in 20 hours, Michael does 20/45 of the needed shells<BR>\n" );
document.write( "20/36+20/45 needs to equal 1 ( all the needed shells, that is)<BR>\n" );
document.write( "20/36 +20/45 =1<BR>\n" );
document.write( "5/9 +4/9=9/9=1 OKKKKKKKKKK\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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