document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=311811>Question 311811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #223010 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=223010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Working together, Rick and Juanita can complete a job in 6 hours.<BR>\n" );
document.write( " It would take Rick 9 hours longer than Juanita to do the job alone.<BR>\n" );
document.write( " How long would it take Juanita alone?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let t = time for J to do it alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t+9) = time for R to do it alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let the completed job = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A shared work equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ft ALIGN=MIDDLE  ALT=\"6%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28t%2B9%29 ALIGN=MIDDLE  ALT=\"6%2F%28t%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply equation by t(t+9), results<BR>\n" );
document.write( "6(t+9) + 6t = t(t+9)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "6t + 54 + 6t = t^2 + 9t<BR>\n" );
document.write( "combine on the right<BR>\n" );
document.write( "0 = t^2 + 9t - 12t - 54<BR>\n" );
document.write( ":<BR>\n" );
document.write( "t^2 - 3t - 54 = 0<BR>\n" );
document.write( "Factor<BR>\n" );
document.write( "(t-9)(t+6) = 0<BR>\n" );
document.write( "positive solution<BR>\n" );
document.write( "t = 9 hrs J, alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "9 + 9 = 18 hrs R alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution<BR>\n" );
document.write( "6/9 + 6/18 = 1\r<BR>\n" );
document.write( "\n" );
document.write( ":<BR>\n" );
document.write( "Note: Rick only has one arm<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );