document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=824509>Question 824509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hayden is the manager  of a landscaping company.  He had three employees to do the entire park, Cody Kaitlin  and Joseph.Cody can complete the job in 8 hrs. kaitlin can complete the project in 6 hours.  Joseph is neew so no one knows how it will take him.  They must all work together to complete the project.  How could I explain to Hayden how long it would take Joseph working by himself? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #496565 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=496565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you add their rates of working, you<BR>\n" );
document.write( "will get their rate of working together<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Cody's rate is ( 1 job ) / ( 8 hrs )<BR>\n" );
document.write( "Kaitlin's rate is ( 1 job ) / ( 6 hrs )<BR>\n" );
document.write( "Let Joseph's rate = ( 1 job ) / ( t hrs )<BR>\n" );
document.write( "Let their rate working together = ( 1 job ) / ( T hrs )<BR>\n" );
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document.write( "I can say:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F8+%2B+1%2F6+%2B+1%2Ft+=+1%2FT+ ALIGN=MIDDLE  ALT=\"+1%2F8+%2B+1%2F6+%2B+1%2Ft+=+1%2FT+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "The time, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+ ALIGN=MIDDLE  ALT=\"+T+\"   DISABLED_style= \"max-width:90%; height:auto;\" > has to be less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+ ALIGN=MIDDLE  ALT=\"+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "no matter how slow Joseph is.<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Suppose Joseph is the slowest and takes <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12+ ALIGN=MIDDLE  ALT=\"+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs to do the job alone<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F8+%2B+1%2F6+%2B+1%2Ft+=+1%2FT+ ALIGN=MIDDLE  ALT=\"+1%2F8+%2B+1%2F6+%2B+1%2Ft+=+1%2FT+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F8+%2B+1%2F6+%2B+1%2F12+=+1%2FT+ ALIGN=MIDDLE  ALT=\"+1%2F8+%2B+1%2F6+%2B+1%2F12+=+1%2FT+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+24T+ ALIGN=MIDDLE  ALT=\"+24T+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3T+%2B+4T+%2B+2T+=+24+ ALIGN=MIDDLE  ALT=\"+3T+%2B+4T+%2B+2T+=+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9T+=+24+ ALIGN=MIDDLE  ALT=\"+9T+=+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+2.667+ ALIGN=MIDDLE  ALT=\"+T+=+2.667+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "If Joseph happens to be faster than the other two,<BR>\n" );
document.write( "the job will get done in LESS than Joseph's time<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "Joseph's rate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F2+ ALIGN=MIDDLE  ALT=\"+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F8+%2B+1%2F6+%2B+1%2Ft+=+1%2FT+ ALIGN=MIDDLE  ALT=\"+1%2F8+%2B+1%2F6+%2B+1%2Ft+=+1%2FT+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F8+%2B+1%2F6+%2B+1%2F2+=+1%2FT+ ALIGN=MIDDLE  ALT=\"+1%2F8+%2B+1%2F6+%2B+1%2F2+=+1%2FT+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3T+%2B+4T+%2B+12T+=+24+ ALIGN=MIDDLE  ALT=\"+3T+%2B+4T+%2B+12T+=+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+19T+=+24+ ALIGN=MIDDLE  ALT=\"+19T+=+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+1.2632+ ALIGN=MIDDLE  ALT=\"+T+=+1.2632+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );