document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=723288>Question 723288</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a king hires a crew of 30 workers, who can build a castle wall in 60 days. However, 10 days after the wall was started, the king decided that the wall must be finished in a total of 40 days. How many additional workers must be hired if all the workers work with the same constant rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443113 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=443113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+ ALIGN=MIDDLE  ALT=\"+R+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the rate at which a single worker works<BR>\n" );
document.write( "Add their rates of working to get their rate<BR>\n" );
document.write( "working together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30R+=+1%2F60+ ALIGN=MIDDLE  ALT=\"+30R+=+1%2F60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F60+ ALIGN=MIDDLE  ALT=\"+1%2F60+\"   DISABLED_style= \"max-width:90%; height:auto;\" > means 1 wall / 60 days )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+1%2F1800+ ALIGN=MIDDLE  ALT=\"+R+=+1%2F1800+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The 30 workers work for 10 days.<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the fraction of the wall they finish<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30R+=+x%2F10+ ALIGN=MIDDLE  ALT=\"+30R+=+x%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F60+=+x%2F10+ ALIGN=MIDDLE  ALT=\"+1%2F60+=+x%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+x+=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, 5/6 of the wall must be finished in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+-+10+=+30+ ALIGN=MIDDLE  ALT=\"+40+-+10+=+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > days<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+ ALIGN=MIDDLE  ALT=\"+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the number of additional workers needed  to<BR>\n" );
document.write( "finish the wall in 30 more days<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+30+%2B+n+%29%2AR+=+%28+5%2F6+%29+%2F+30+ ALIGN=MIDDLE  ALT=\"+%28+30+%2B+n+%29%2AR+=+%28+5%2F6+%29+%2F+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30R+%2B+n%2AR+=+5%2F180+ ALIGN=MIDDLE  ALT=\"+30R+%2B+n%2AR+=+5%2F180+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%2AR+=+5%2F180+-+1%2F60+ ALIGN=MIDDLE  ALT=\"+n%2AR+=+5%2F180+-+1%2F60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+1%2F1800+ ALIGN=MIDDLE  ALT=\"+R+=+1%2F1800+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%2A%28+1%2F1800+%29+=+50+%2F+1800+-+30%2F1800+ ALIGN=MIDDLE  ALT=\"+n%2A%28+1%2F1800+%29+=+50+%2F+1800+-+30%2F1800+\"   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=+1800+ ALIGN=MIDDLE  ALT=\"+1800+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+20+ ALIGN=MIDDLE  ALT=\"+n+=+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "20 workers must be added to finish in 40 days<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "can <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+%2B+20+=+50+ ALIGN=MIDDLE  ALT=\"+30+%2B+20+=+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" > workers do 5/6 of the wall<BR>\n" );
document.write( "in 30 days?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50R+=+%28+5%2F6+%29+%2F+30+ ALIGN=MIDDLE  ALT=\"+50R+=+%28+5%2F6+%29+%2F+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50%2A180%2AR+=+5+ ALIGN=MIDDLE  ALT=\"+50%2A180%2AR+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+5+%2F+9000+ ALIGN=MIDDLE  ALT=\"+R+=+5+%2F+9000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+1%2F1800+ ALIGN=MIDDLE  ALT=\"+R+=+1%2F1800+\"   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" );