document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=486794>Question 486794</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Working together, two men can do a job in 20 days. Working alone, however, it would take one man 9 days longer than it would take the other to complete the job. How long would it take each separately? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333030 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=333030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Working together, two men can do a job in 20 days. <BR>\n" );
document.write( "Working alone, however, it would take one man 9 days longer than it would take the other to complete the job.<BR>\n" );
document.write( " How long would it take each separately?<BR>\n" );
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document.write( "Let t = time required by the 1st man to do the job alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t+9) = time required by the 2nd man alone<BR>\n" );
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document.write( "Let the completed job = 1<BR>\n" );
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document.write( "A typical shared work equation<BR>\n" );
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document.write( "Each man will do a fraction of the job, the two fractions add up to 1<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2Ft ALIGN=MIDDLE  ALT=\"20%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F%28t%2B9%29 ALIGN=MIDDLE  ALT=\"20%2F%28t%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "multiply by t(t+9), results<BR>\n" );
document.write( "20(t+9) + 20t = t(t+9)<BR>\n" );
document.write( "20t + 180 + 20t = t^2 + 9t<BR>\n" );
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document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "t^2 + 9t - 40t - 180 = 0<BR>\n" );
document.write( "t^2 - 31t - 180 = 0<BR>\n" );
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document.write( "you can solve this using the quadratic equation, but it will factor to:<BR>\n" );
document.write( "(t-36)(t+5) = 0<BR>\n" );
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document.write( "the positive solution<BR>\n" );
document.write( "t = 36 days required by the 1st man<BR>\n" );
document.write( "then<BR>\n" );
document.write( "36 + 9 = 45 days required by the 2nd man<BR>\n" );
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document.write( "Check this<BR>\n" );
document.write( "20/36  + 20/45<BR>\n" );
document.write( ".56 + .44 = 1<BR>\n" );
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