document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697146>Question 697146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two old machines and a new one are put to work on a contract. Each of the old ones requires twice as much time as the new one to do the job. Together, the three machines complete the work in 2 days. How long would it take each machine to do the work alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429706 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=429706\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Add their rates of working to get their<BR>\n" );
document.write( "rate working together<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the rate for an old machine<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B2%5D+ ALIGN=MIDDLE  ALT=\"+r%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the rate for a new machine<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+=+%281%2F2%29%2Ar%5B2%5D+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+=+%281%2F2%29%2Ar%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Note that twice the time means half the rate<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Given: 3 machines working together have<BR>\n" );
document.write( "a rate of ( 1 contract ) / ( 2 days )<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+%2B+r%5B1%5D+%2B+r%5B2%5D+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+%2B+r%5B1%5D+%2B+r%5B2%5D+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2r%5B1%5D+%2B+r%5B2%5D+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+2r%5B1%5D+%2B+r%5B2%5D+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute (1) into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%281%2F2%29%2Ar%5B2%5D+%2B+r%5B2%5D+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+2%2A%281%2F2%29%2Ar%5B2%5D+%2B+r%5B2%5D+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B2%5D+%2B+r%5B2%5D+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+r%5B2%5D+%2B+r%5B2%5D+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2r%5B2%5D+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+2r%5B2%5D+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B2%5D+=+1%2F4+ ALIGN=MIDDLE  ALT=\"+r%5B2%5D+=+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+=+%281%2F2%29%2Ar%5B2%5D+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+=+%281%2F2%29%2Ar%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+=+%281%2F2%29%2A%281%2F4%29+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+=+%281%2F2%29%2A%281%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+=+1%2F8+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+=+1%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Each old machine takes 8 days to do the work alone<BR>\n" );
document.write( "Each new machine takes 4 days to do the work alone<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2r%5B1%5D+%2B+r%5B2%5D+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+2r%5B1%5D+%2B+r%5B2%5D+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%281%2F8%29+%2B+1%2F4+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+2%2A%281%2F8%29+%2B+1%2F4+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+%2B+1%2F4+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+1%2F4+%2B+1%2F4+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F2+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+1%2F2+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );