document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=602226>Question 602226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Larry and Margee can paint a room in 7 hours.  If Margee worked alone it would take her 3 hours longer than if Larry worked alone.  How long would it take each person if they worked alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #380336 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=380336\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Larry and Margee can paint a room in 7 hours.<BR>\n" );
document.write( " If Margee worked alone it would take her 3 hours longer than if Larry worked alone.<BR>\n" );
document.write( " How long would it take each person if they worked alone?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let t = L's time to do the job alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t=3) = M's time to do it<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let completed job = 1 (a painted room)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Ft ALIGN=MIDDLE  ALT=\"7%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28%28t%2B3%29%29 ALIGN=MIDDLE  ALT=\"7%2F%28%28t%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply by t(t+3) to clear the denominators, results<BR>\n" );
document.write( "7(t+3) + 7t = t(t+3)<BR>\n" );
document.write( "7t + 21 + 7t = t^2 + 3t<BR>\n" );
document.write( "14t + 21  = t^2 + 3t<BR>\n" );
document.write( "0 = t^2 + 3t - 14t - 21<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "t^2 - 11t - 21 = 0<BR>\n" );
document.write( "use the quadratic formula to find t<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "In this equation: x=t; a=1; b=-11; c=-21<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%28-11%29+%2B-+sqrt%28-11%5E2-4%2A1%2A-21+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-%28-11%29+%2B-+sqrt%28-11%5E2-4%2A1%2A-21+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2811+%2B-+sqrt%28121%2B84+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"t+=+%2811+%2B-+sqrt%28121%2B84+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2811+%2B-+sqrt%28205+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"t+=+%2811+%2B-+sqrt%28205+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The positive solution<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2811+%2B+14.3%29%2F2+ ALIGN=MIDDLE  ALT=\"t+=+%2811+%2B+14.3%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25.3%2F2 ALIGN=MIDDLE  ALT=\"25.3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 12.65 hrs, time L takes working alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "12.65+3 = 15.65 hrs, time M takes working alone<BR>\n" );
document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );