document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=631013>Question 631013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> After 5 hours of painting, Jess asked the assistance of Jon. Together they finished the job in 4 more hours. Had Jon joined in an hour after Jess started working, the job would have been finished in 7 hours. How long would it have taken Jess to paint the house alone </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #397344 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=397344\">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%5B1%5D+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Jess's rate of painting in jobs/hr<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;\" > = Jon's rate of painting in jobs/hr<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "In 5 hours Jess gets <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5r%5B1%5D+ ALIGN=MIDDLE  ALT=\"+5r%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > fraction of the job done<BR>\n" );
document.write( "In 1 hour jess get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Ar%5B1%5D+ ALIGN=MIDDLE  ALT=\"+1%2Ar%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > fraction of the job done<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5r%5B1%5D+%2B+4%2A%28+r%5B1%5D+%2B+r%5B2%5D+%29+=+1+ ALIGN=MIDDLE  ALT=\"+5r%5B1%5D+%2B+4%2A%28+r%5B1%5D+%2B+r%5B2%5D+%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( 1 means the whole job is done )<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Ar%5B1%5D+%2B+7%2A%28+r%5B1%5D+%2B+r%5B2%5D+%29+=+1+ ALIGN=MIDDLE  ALT=\"+1%2Ar%5B1%5D+%2B+7%2A%28+r%5B1%5D+%2B+r%5B2%5D+%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9r%5B1%5D+%2B+4r%5B2%5D+=+1+ ALIGN=MIDDLE  ALT=\"+9r%5B1%5D+%2B+4r%5B2%5D+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8r%5B1%5D+%2B+7r%5B2%5D+=+1+ ALIGN=MIDDLE  ALT=\"+8r%5B1%5D+%2B+7r%5B2%5D+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Multiply both sides of (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7+ ALIGN=MIDDLE  ALT=\"+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides of (2) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+ ALIGN=MIDDLE  ALT=\"+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and subtract (2) from (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+63r%5B1%5D+%2B+28r%5B2%5D+=+7+ ALIGN=MIDDLE  ALT=\"+63r%5B1%5D+%2B+28r%5B2%5D+=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-32r%5B1%5D+-+28r%5B2%5D+=+-4+ ALIGN=MIDDLE  ALT=\"+-32r%5B1%5D+-+28r%5B2%5D+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+31r%5B1%5D+=+3+ ALIGN=MIDDLE  ALT=\"+31r%5B1%5D+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+=+3%2F31+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+=+3%2F31+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This means Jess can paint 3 houses in 31 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F31+=+1%2Fx+ ALIGN=MIDDLE  ALT=\"+3%2F31+=+1%2Fx+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10.333+ ALIGN=MIDDLE  ALT=\"+10.333+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "He could paint the house alone in 10 hrs and 20 min<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9%2A%283%2F31%29+%2B+4r%5B2%5D+=+1+ ALIGN=MIDDLE  ALT=\"+9%2A%283%2F31%29+%2B+4r%5B2%5D+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4r%5B2%5D+=+31%2F31+-+27%2F31+ ALIGN=MIDDLE  ALT=\"+4r%5B2%5D+=+31%2F31+-+27%2F31+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4r%5B2%5D+=+4%2F31+ ALIGN=MIDDLE  ALT=\"+4r%5B2%5D+=+4%2F31+\"   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%5B2%5D+=+1%2F31+ ALIGN=MIDDLE  ALT=\"+r%5B2%5D+=+1%2F31+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8%2A%283%2F31%29+%2B+7%2A%281%2F31%29+=+1+ ALIGN=MIDDLE  ALT=\"+8%2A%283%2F31%29+%2B+7%2A%281%2F31%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+24%2F31+%2B+7%2F31+=+31%2F31+ ALIGN=MIDDLE  ALT=\"+24%2F31+%2B+7%2F31+=+31%2F31+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+24+%2B+7+=+31+ ALIGN=MIDDLE  ALT=\"+24+%2B+7+=+31+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+31+=+31+ ALIGN=MIDDLE  ALT=\"+31+=+31+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );