document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089967>Question 1089967</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ralph paints a room in k hours, Jenny paints the room in m hours.  Jenny takes two more hours to paint than Ralph.  Together they can paint in 8 hours.  How many hours can each paint the room on their own.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704374 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704374\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rate x Time = Output <BR>\n" );
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document.write( "Let's say that an output of 100 is required for the room to be painted (this number is arbitrary).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5BR%5D%2Ak=100 ALIGN=MIDDLE  ALT=\"R%5BR%5D%2Ak=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5BR%5D=100%2Fk ALIGN=MIDDLE  ALT=\"R%5BR%5D=100%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5BJ%5D%2Am=100 ALIGN=MIDDLE  ALT=\"R%5BJ%5D%2Am=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5BJ%5D=100%2Fm ALIGN=MIDDLE  ALT=\"R%5BJ%5D=100%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=k%2B2 ALIGN=MIDDLE  ALT=\"m=k%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%5BR%5D%2BR%5BJ%5D%298=100 ALIGN=MIDDLE  ALT=\"%28R%5BR%5D%2BR%5BJ%5D%298=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5BR%5D%2BR%5BJ%5D=25%2F2 ALIGN=MIDDLE  ALT=\"R%5BR%5D%2BR%5BJ%5D=25%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2Fk%2B100%2Fm=25%2F2 ALIGN=MIDDLE  ALT=\"100%2Fk%2B100%2Fm=25%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Fk%2B8%2Fm=1 ALIGN=MIDDLE  ALT=\"8%2Fk%2B8%2Fm=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Fk%2B8%2F%28k%2B2%29=1 ALIGN=MIDDLE  ALT=\"8%2Fk%2B8%2F%28k%2B2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8k%2B8%28k%2B2%29=k%28k%2B2%29 ALIGN=MIDDLE  ALT=\"8k%2B8%28k%2B2%29=k%28k%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8k%2B8k%2B16=k%5E2%2B2k ALIGN=MIDDLE  ALT=\"8k%2B8k%2B16=k%5E2%2B2k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2-14k-16=0 ALIGN=MIDDLE  ALT=\"k%5E2-14k-16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Completing the square,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%5E2-14k%2B49%29-16=49 ALIGN=MIDDLE  ALT=\"%28k%5E2-14k%2B49%29-16=49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k-7%29%5E2=65 ALIGN=MIDDLE  ALT=\"%28k-7%29%5E2=65\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k-7=0+%2B-+sqrt%2865%29 ALIGN=MIDDLE  ALT=\"k-7=0+%2B-+sqrt%2865%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=7+%2B-+sqrt%2865%29 ALIGN=MIDDLE  ALT=\"k=7+%2B-+sqrt%2865%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Only positive values of k are acceptable for this problem.<BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5BR%5D=7%2Bsqrt%2865%29 ALIGN=MIDDLE  ALT=\"R%5BR%5D=7%2Bsqrt%2865%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5BJ%5D=7%2Bsqrt%2865%29%2B2=9%2Bsqrt%2865%29 ALIGN=MIDDLE  ALT=\"R%5BJ%5D=7%2Bsqrt%2865%29%2B2=9%2Bsqrt%2865%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );