document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4363>Question 4363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are three friends named Allan, Bobby and Charlie. The three friends want to know their individual rate in finishing a job. Allan and Bobby can finish the job in 42 days, Bobby and Charlie can finish the job in 31 days, and Allan and Charlie can finish the job in 20 days. Solve the rate of each individual.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1980 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=1980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A = number of days it would take Allan to do the job alone,<BR>\n" );
document.write( "Let B = number of days it would take Bobby to do the job alone, and<BR>\n" );
document.write( "Let C = number of days it would take Charlie to do the job alone.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FA ALIGN=MIDDLE  ALT=\"1%2FA\"   DISABLED_style= \"max-width:90%; height:auto;\" > = part of the job that Allan can do in 1 day,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FB ALIGN=MIDDLE  ALT=\"1%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" > = part of the job that Bobby can do in 1 day, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FC ALIGN=MIDDLE  ALT=\"1%2FC\"   DISABLED_style= \"max-width:90%; height:auto;\" > = part of the job that Charlie can do in 1 day.\r<BR>\n" );
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document.write( "Also given in the problem, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F42 ALIGN=MIDDLE  ALT=\"1%2F42\"   DISABLED_style= \"max-width:90%; height:auto;\" > = part of the job that Allan and Bobby can do in 1 day,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F31 ALIGN=MIDDLE  ALT=\"1%2F31\"   DISABLED_style= \"max-width:90%; height:auto;\" > = part of the job that Bobby and Charlie can do in 1 day, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F20 ALIGN=MIDDLE  ALT=\"1%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = part of the job that Allan and Charlie can do in 1 day.\r<BR>\n" );
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document.write( "There are three unknowns, so there must be three equations to solve:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FA+%2B+1%2FB+=+1%2F42 ALIGN=MIDDLE  ALT=\"1%2FA+%2B+1%2FB+=+1%2F42\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = Equation #1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FB+%2B+1%2FC+=+1%2F31 ALIGN=MIDDLE  ALT=\"1%2FB+%2B+1%2FC+=+1%2F31\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = Equation #2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FA+%2B+1%2FC+=+1%2F20 ALIGN=MIDDLE  ALT=\"1%2FA+%2B+1%2FC+=+1%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = Equation #3\r<BR>\n" );
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document.write( "To eliminate one of these unknowns, Subract Equation #2 - Equation #3, which eliminates the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FC ALIGN=MIDDLE  ALT=\"1%2FC\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FB-1%2FA+=+1%2F31+-+1%2F20 ALIGN=MIDDLE  ALT=\"1%2FB-1%2FA+=+1%2F31+-+1%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To this equation, now add Equation #1, which eliminates the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FA ALIGN=MIDDLE  ALT=\"1%2FA\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FB-1%2FA+=+1%2F31+-+1%2F20 ALIGN=MIDDLE  ALT=\"1%2FB-1%2FA+=+1%2F31+-+1%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FA+%2B+1%2FB+=+1%2F42 ALIGN=MIDDLE  ALT=\"1%2FA+%2B+1%2FB+=+1%2F42\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FB+%2B+1%2FB+=+1%2F31+-+1%2F20+%2B+1%2F42 ALIGN=MIDDLE  ALT=\"1%2FB+%2B+1%2FB+=+1%2F31+-+1%2F20+%2B+1%2F42\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finding a least common denominator for denominators like 31, 20, and 42 is harder than just using the product of the denominators, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31%2A20%2A42 ALIGN=MIDDLE  ALT=\"31%2A20%2A42\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 26040.  The result is as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2FB+=+%281%2F31%29+%2A+%28%2820%2A42%29%2F%2820%2A42%29%29+-+%281%2F20%29+%2A+%28%2831%2A42%29%2F%2831%2A42%29%29+%2B+%281%2F42%29+%2A%28%2831%2A20%29%2F%2831%2A20%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2FB+=+%2820%2A42+-+31%2A42+%2B+31%2A20%29+%2F+%2831%2A20%2A42%29+ ALIGN=MIDDLE  ALT=\"+2%2FB+=+%2820%2A42+-+31%2A42+%2B+31%2A20%29+%2F+%2831%2A20%2A42%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2FB+=+%28840-+1302+%2B+620%29+%2F+%2831%2A20%2A42%29+ ALIGN=MIDDLE  ALT=\"+2%2FB+=+%28840-+1302+%2B+620%29+%2F+%2831%2A20%2A42%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2FB+=+%28158%29+%2F+%2831%2A20%2A42%29+ ALIGN=MIDDLE  ALT=\"+2%2FB+=+%28158%29+%2F+%2831%2A20%2A42%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides by 2, giving\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2FB+=+%2879%29+%2F+%2831%2A20%2A42%29+ ALIGN=MIDDLE  ALT=\"+1%2FB+=+%2879%29+%2F+%2831%2A20%2A42%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find B, take the reciprocal of both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=+%2831%2A20%2A42%29%2F79+ ALIGN=MIDDLE  ALT=\"B=+%2831%2A20%2A42%29%2F79+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is approximately 330 days.\r<BR>\n" );
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document.write( "To find A,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FA+=+1%2F42+-+1%2FB ALIGN=MIDDLE  ALT=\"1%2FA+=+1%2F42+-+1%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FA+=+1%2F42+-+79%2F%2831%2A20%2A42%29 ALIGN=MIDDLE  ALT=\"1%2FA+=+1%2F42+-+79%2F%2831%2A20%2A42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FA+=+%28%2831%2A20%29+-+79%29%2F+%2831%2A20%2A42%29 ALIGN=MIDDLE  ALT=\"1%2FA+=+%28%2831%2A20%29+-+79%29%2F+%2831%2A20%2A42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FA+=+541%2F+%2831%2A20%2A42%29+ ALIGN=MIDDLE  ALT=\"1%2FA+=+541%2F+%2831%2A20%2A42%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%2831%2A20%2A42%29%2F541 ALIGN=MIDDLE  ALT=\"A+=+%2831%2A20%2A42%29%2F541\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which is approximately 48 days.\r<BR>\n" );
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document.write( "To find C\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FC=+1%2F31+-1%2FB ALIGN=MIDDLE  ALT=\"1%2FC=+1%2F31+-1%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FC=+1%2F31-79%2F%2831%2A20%2A42%29 ALIGN=MIDDLE  ALT=\"1%2FC=+1%2F31-79%2F%2831%2A20%2A42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FC=+%28%2842%2A20%29-+79%29%2F+%2831%2A20%2A42%29 ALIGN=MIDDLE  ALT=\"1%2FC=+%28%2842%2A20%29-+79%29%2F+%2831%2A20%2A42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FC+=+761%2F+%2831%2A20%2A42%29+ ALIGN=MIDDLE  ALT=\"1%2FC+=+761%2F+%2831%2A20%2A42%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+%2831%2A20%2A42%29%2F761 ALIGN=MIDDLE  ALT=\"C+=+%2831%2A20%2A42%29%2F761\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which is approximately 34 days.\r<BR>\n" );
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document.write( "[NOTE:  Where did you get this problem??  If I had known when I started this problem that it would have been this complicated, I would have left it for Kenny!!  There is probably an easier way to do this.  Ask him!!]\r<BR>\n" );
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document.write( "R^2 at SCC\r<BR>\n" );
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document.write( " </SPAN>\n" );
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