document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=917391>Question 917391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 8 men and 16 women can do a work in 8 days.40 men and 48 women can do the same work in 2 days.how many days are required for 6 men and 12 women to do the same work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556641 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=556641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let m = how many days 1 man could do the work if alone;<BR>\n" );
document.write( "let w = how many ways 1 woman could do the same work alone.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%288%281%2Fm%29%2B16%281%2Fw%29%2940=1%29 ALIGN=MIDDLE  ALT=\"cross%28%288%281%2Fm%29%2B16%281%2Fw%29%2940=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%2840%281%2Fm%29%2B48%281%2Fw%29%292=1%29 ALIGN=MIDDLE  ALT=\"cross%28%2840%281%2Fm%29%2B48%281%2Fw%29%292=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Two equations, two unknown variables; simplify each equation and solve the system.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first arrangement of workers<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2Fm%2B16%2Fw%298=1 ALIGN=MIDDLE  ALT=\"%288%2Fm%2B16%2Fw%298=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to account for 1 job<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2Fm%2B128%2Fw=1 ALIGN=MIDDLE  ALT=\"64%2Fm%2B128%2Fw=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and LCD is mw<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64w%2B128m=mw ALIGN=MIDDLE  ALT=\"64w%2B128m=mw\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Second arrangement of workers<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2840%2Fm%2B48%2Fw%292=1 ALIGN=MIDDLE  ALT=\"%2840%2Fm%2B48%2Fw%292=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2Fm%2B96%2Fw=1 ALIGN=MIDDLE  ALT=\"80%2Fm%2B96%2Fw=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80w%2B96m=mw ALIGN=MIDDLE  ALT=\"80w%2B96m=mw\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Two equal formulas for mw.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64w%2B128m=80w%2B96m ALIGN=MIDDLE  ALT=\"64w%2B128m=80w%2B96m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32m=16w ALIGN=MIDDLE  ALT=\"32m=16w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m=w ALIGN=MIDDLE  ALT=\"2m=w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the relationship between m and w, which through substitution,<BR>\n" );
document.write( "allows to find through either of the mw equations, to solve for w and m,<BR>\n" );
document.write( "the NUMBER OF DAYS for one woman to do one job and the NUMBER OF DAYS for one man to do one job.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use this system:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28system%2864w%2B128m=mw%2C90w%2B96m=mw%2Cw=2m%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28system%2864w%2B128m=mw%2C90w%2B96m=mw%2Cw=2m%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(Further steps, not yet done, but you need to do them.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can then answer the actual question from there, using RT=J for <BR>\n" );
document.write( "rate time job, uniform work rates formula. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=2m ALIGN=MIDDLE  ALT=\"w=2m\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64w%2B128m=mw ALIGN=MIDDLE  ALT=\"64w%2B128m=mw\"   DISABLED_style= \"max-width:90%; height:auto;\" >, solving for m gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28m=128%29 ALIGN=MIDDLE  ALT=\"highlight%28m=128%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > days and this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=256%29 ALIGN=MIDDLE  ALT=\"highlight%28w=256%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > days.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, use those to solve the question asked.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Rate in jobs per day for the 6 men and 12 women,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2F128%2B12%2F256%29 ALIGN=MIDDLE  ALT=\"%286%2F128%2B12%2F256%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let t be the number of days for this group to do 1 job.<BR>\n" );
document.write( "The uniform rates rule gives:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%286%2F128%2B12%2F256%29t=1%29 ALIGN=MIDDLE  ALT=\"highlight%28%286%2F128%2B12%2F256%29t=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for t.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "-<BR>\n" );
document.write( "RESULT:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=10%262%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28t=10%262%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > days. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );