document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=722406>Question 722406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> aron, Brenda, Charlie, and Danita are house painters. The team of Aaron, Brenda, and Charlie can paint my house in 3 days; if Aaron and Danita work as a pair it takes 6 days; the pair of Charlie and Danita takes 8 days, and the team of Brenda, Charlie, and Danit can finish in 5 days. How long would it take the whole 4-person crew to paint my house? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #442761 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=442761\">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%5Ba%5D+ ALIGN=MIDDLE  ALT=\"+r%5Ba%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Aaron's rate of painting in houses/day<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Bb%5D+ ALIGN=MIDDLE  ALT=\"+r%5Bb%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Brenda's rate of painting in houses/day<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Bc%5D+ ALIGN=MIDDLE  ALT=\"+r%5Bc%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Charlie's rate of painting in houses/day<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Bd%5D+ ALIGN=MIDDLE  ALT=\"+r%5Bd%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Danita's rate of painting in houses/day<BR>\n" );
document.write( "----------------------------------------------<BR>\n" );
document.write( "Add rates to get the rate working together<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Ba%5D+%2B+r%5Bb%5D+%2B+r%5Bc%5D+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+r%5Ba%5D+%2B+r%5Bb%5D+%2B+r%5Bc%5D+=+1%2F3+\"   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%5Ba%5D+%2B+r%5Bd%5D+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+r%5Ba%5D+%2B+r%5Bd%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%5Bc%5D+%2B+r%5Bd%5D+=+1%2F8+ ALIGN=MIDDLE  ALT=\"+r%5Bc%5D+%2B+r%5Bd%5D+=+1%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Bb%5D+%2B+r%5Bc%5D+%2B+r%5Bd%5D+=+1%2F5+ ALIGN=MIDDLE  ALT=\"+r%5Bb%5D+%2B+r%5Bc%5D+%2B+r%5Bd%5D+=+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "This is 4 equations and 4 unknowns, so it should be solvable<BR>\n" );
document.write( "Subtract (4) from (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Ba%5D+%2B+r%5Bb%5D+%2B+r%5Bc%5D+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+r%5Ba%5D+%2B+r%5Bb%5D+%2B+r%5Bc%5D+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-r%5Bd%5D+-+r%5Bb%5D+-+r%5Bc%5D+=+-1%2F5+ ALIGN=MIDDLE  ALT=\"+-r%5Bd%5D+-+r%5Bb%5D+-+r%5Bc%5D+=+-1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Ba%5D+-+r%5Bd%5D+=+5%2F15+-+3%2F15+ ALIGN=MIDDLE  ALT=\"+r%5Ba%5D+-+r%5Bd%5D+=+5%2F15+-+3%2F15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Ba%5D+-+r%5Bd%5D+=+2%2F15+ ALIGN=MIDDLE  ALT=\"+r%5Ba%5D+-+r%5Bd%5D+=+2%2F15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Add this result to (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Ba%5D+%2B+r%5Bd%5D+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+r%5Ba%5D+%2B+r%5Bd%5D+=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Ba%5D+-+r%5Bd%5D+=+2%2F15+ ALIGN=MIDDLE  ALT=\"+r%5Ba%5D+-+r%5Bd%5D+=+2%2F15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2r%5Ba%5D+=+5%2F30+%2B+4%2F30+ ALIGN=MIDDLE  ALT=\"+2r%5Ba%5D+=+5%2F30+%2B+4%2F30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2r%5Ba%5D+=+1%2F30+ ALIGN=MIDDLE  ALT=\"+2r%5Ba%5D+=+1%2F30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Ba%5D+=+1%2F60+ ALIGN=MIDDLE  ALT=\"+r%5Ba%5D+=+1%2F60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5Ba%5D+%2B+r%5Bd%5D+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+r%5Ba%5D+%2B+r%5Bd%5D+=+1%2F6+\"   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%2F60+%2B+r%5Bd%5D+=+1%2F6+ ALIGN=MIDDLE  ALT=\"+1%2F60+%2B+r%5Bd%5D+=+1%2F6+\"   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%5Bd%5D+=+10%2F60+-+1%2F60+ ALIGN=MIDDLE  ALT=\"+r%5Bd%5D+=+10%2F60+-+1%2F60+\"   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%5Bd%5D+=+9%2F60+ ALIGN=MIDDLE  ALT=\"+r%5Bd%5D+=+9%2F60+\"   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%5Bd%5D+=+3%2F20+ ALIGN=MIDDLE  ALT=\"+r%5Bd%5D+=+3%2F20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can finish- have to go<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );