document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=387082>Question 387082</A>: <I><SPAN STYLE=\"word-break: break-all;\"> IT WOULD TAKE BETSEY 4 HOURS TO CLEAN HER ROOM. HER MOM COULD DO IT IN 2 HOURS. USE ALGEBRA TO FIND HOW LONG IT WOULD TAKE THEM WORKING TOGETHER? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #273616 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=273616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Think of these problems as adding their<BR>\n" );
document.write( "rates of working separately<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D ALIGN=MIDDLE  ALT=\"R%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Betsy's rate of working alone<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D ALIGN=MIDDLE  ALT=\"R%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Mother's rate of working alone<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B3%5D ALIGN=MIDDLE  ALT=\"R%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = their rate of working together<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "The rule is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D+%2B+R%5B2%5D+=+R%5B3%5D ALIGN=MIDDLE  ALT=\"R%5B1%5D+%2B+R%5B2%5D+=+R%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B1%5D+=+1%2F4 ALIGN=MIDDLE  ALT=\"R%5B1%5D+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This means 1 room cleaned in 4 hours<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D+=+1%2F2 ALIGN=MIDDLE  ALT=\"R%5B2%5D+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This means 1 room cleaned in 2 hours<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "So far I've got<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4+%2B+1%2F2+=+R%5B3%5D ALIGN=MIDDLE  ALT=\"1%2F4+%2B+1%2F2+=+R%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can express <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B3%5D ALIGN=MIDDLE  ALT=\"R%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or 1 room<BR>\n" );
document.write( "cleaned in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours<BR>\n" );
document.write( "Now I have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4+%2B+1%2F2+=+1%2Fx ALIGN=MIDDLE  ALT=\"1%2F4+%2B+1%2F2+=+1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+2x+=+4 ALIGN=MIDDLE  ALT=\"x+%2B+2x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+=+4 ALIGN=MIDDLE  ALT=\"3x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4%2F3 ALIGN=MIDDLE  ALT=\"x+=+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours<BR>\n" );
document.write( "This is the same as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29%2A60+=+80 ALIGN=MIDDLE  ALT=\"%284%2F3%29%2A60+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" > min, or 1 hour and 20 minutes working together </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );