document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=731272>Question 731272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Andrew, Beth, and Carlos are painting a house. If Andrew and Beth paint the house together, it will take 10 days. If Beth and Carlos paint the house together , it will take 6 days. If Andrew, Beth and Carlos all paint together, it will take 5 days. How long will it take Carlos 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 #447072 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=447072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Add rates of painting to get rate of <BR>\n" );
document.write( "painting together<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Andrew's time in days to paint house alone<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+ ALIGN=MIDDLE  ALT=\"+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Beth's time in days  to paint house alone<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+ ALIGN=MIDDLE  ALT=\"+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Carlos's time in days  to paint house alone<BR>\n" );
document.write( "For example:<BR>\n" );
document.write( "( 1 house ) / ( a days ) + ( 1 house ) / ( b days ) = ( 1 house ) / ( 10 days )<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Fa+%2B+1%2Fb+=+1%2F10+ ALIGN=MIDDLE  ALT=\"+1%2Fa+%2B+1%2Fb+=+1%2F10+\"   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%2Fb+%2B+1%2Fc+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+1%2Fb+%2B+1%2Fc+=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Fa+%2B+1%2Fb+%2B+1%2Fc+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+1%2Fa+%2B+1%2Fb+%2B+1%2Fc+=+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "make these substitutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Fa+=+R%5Ba%5D+ ALIGN=MIDDLE  ALT=\"+1%2Fa+=+R%5Ba%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Fb+=+R%5Bb%5D+ ALIGN=MIDDLE  ALT=\"+1%2Fb+=+R%5Bb%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Fc+=+R%5Bc%5D+ ALIGN=MIDDLE  ALT=\"+1%2Fc+=+R%5Bc%5D+\"   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=+R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F10+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+%2B+R%5Bb%5D+=+1%2F10+\"   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%5Bb%5D+%2B+R%5Bc%5D+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+R%5Bb%5D+%2B+R%5Bc%5D+=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+%2B+R%5Bb%5D+%2B+R%5Bc%5D+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+%2B+R%5Bb%5D+%2B+R%5Bc%5D+=+1%2F5+\"   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=+R%5Ba%5D+=+1%2F10+-+R%5Bb%5D+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+=+1%2F10+-+R%5Bb%5D+\"   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=+R%5Bc%5D+=+1%2F6+-+R%5Bb%5D+ ALIGN=MIDDLE  ALT=\"+R%5Bc%5D+=+1%2F6+-+R%5Bb%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F10+-+R%5Bb%5D+%2B+R%5Bb%5D+%2B+1%2F6+-+R%5Bb%5D+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+1%2F10+-+R%5Bb%5D+%2B+R%5Bb%5D+%2B+1%2F6+-+R%5Bb%5D+=+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bb%5D+=+1%2F10+%2B+1%2F6+-+1%2F5+ ALIGN=MIDDLE  ALT=\"+R%5Bb%5D+=+1%2F10+%2B+1%2F6+-+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bb%5D+=+3%2F30+%2B+5%2F30+-+6%2F30+ ALIGN=MIDDLE  ALT=\"+R%5Bb%5D+=+3%2F30+%2B+5%2F30+-+6%2F30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bb%5D+=+2%2F30+ ALIGN=MIDDLE  ALT=\"+R%5Bb%5D+=+2%2F30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bb%5D+=+1%2F15+ ALIGN=MIDDLE  ALT=\"+R%5Bb%5D+=+1%2F15+\"   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=+R%5Bc%5D+=+1%2F6+-+R%5Bb%5D+ ALIGN=MIDDLE  ALT=\"+R%5Bc%5D+=+1%2F6+-+R%5Bb%5D+\"   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%5Bc%5D+=+1%2F6+-+1%2F15+ ALIGN=MIDDLE  ALT=\"+R%5Bc%5D+=+1%2F6+-+1%2F15+\"   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%5Bc%5D+=+15%2F90+-+6%2F90+ ALIGN=MIDDLE  ALT=\"+R%5Bc%5D+=+15%2F90+-+6%2F90+\"   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%5Bc%5D+=+9%2F90+ ALIGN=MIDDLE  ALT=\"+R%5Bc%5D+=+9%2F90+\"   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%5Bc%5D+=+1%2F10+ ALIGN=MIDDLE  ALT=\"+R%5Bc%5D+=+1%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It will take Carlos 10 days to paint the house alone<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+=+1%2F10+-+R%5Bb%5D+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+=+1%2F10+-+R%5Bb%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%5Ba%5D+=+1%2F10+-+1%2F15+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+=+1%2F10+-+1%2F15+\"   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%5Ba%5D+=+3%2F30+-+2%2F30+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+=+3%2F30+-+2%2F30+\"   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%5Ba%5D+=+1%2F30+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+=+1%2F30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Ba%5D+%2B+R%5Bb%5D+%2B+R%5Bc%5D+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+R%5Ba%5D+%2B+R%5Bb%5D+%2B+R%5Bc%5D+=+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F30+%2B+1%2F15+%2B+1%2F10+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+1%2F30+%2B+1%2F15+%2B+1%2F10+=+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F30+%2B+2%2F30+%2B+3%2F30+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+1%2F30+%2B+2%2F30+%2B+3%2F30+=+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2F30+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+6%2F30+=+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F5+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+1%2F5+=+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );