document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006498>Question 1006498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cistern can be filled by two pipes. The small pipe alone will take 24 minutes longer than the larger pipe to fill the cistern alone. The small pipe alone will take 32 minutes longer to fill the cistern alone when the two pipes are operating together. How long will it take for the larger pipe to fill the cistern alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622647 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=622647\">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=+t%5B1%5D+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time in minutes for the larger pipe<BR>\n" );
document.write( "to fill cistern when filling alone<BR>\n" );
document.write( "Rate of filling = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Ft%5B1%5D+ ALIGN=MIDDLE  ALT=\"+1%2Ft%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time in minutes for both pipes to<BR>\n" );
document.write( "fill cistern when filling together<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+%2B+24+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+%2B+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time in minutes for smaller pipe to <BR>\n" );
document.write( "fill cistern when filling alone<BR>\n" );
document.write( "Rate of filling = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%28+t%5B1%5D+%2B+24+%29+ ALIGN=MIDDLE  ALT=\"+1%2F%28+t%5B1%5D+%2B+24+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+%2B+32+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+%2B+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = this is also time in minutes for smaller pipe to <BR>\n" );
document.write( "fill cistern when filling alone<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+%2B+24+=+t%5B2%5D+%2B+32+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+%2B+24+=+t%5B2%5D+%2B+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+=+t%5B1%5D+-+8+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+=+t%5B1%5D+-+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Add their rates of filling alone to get rate filling together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Ft%5B1%5D+%2B+1%2F%28+t%5B1%5D+%2B+24+%29+=+1%2F%28+t%5B1%5D+-+8+%29+ ALIGN=MIDDLE  ALT=\"+1%2Ft%5B1%5D+%2B+1%2F%28+t%5B1%5D+%2B+24+%29+=+1%2F%28+t%5B1%5D+-+8+%29+\"   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=+t%5B1%5D%2A%28+t%5B1%5D+%2B+24+%29%2A%28+t%5B1%5D+-+8+%29+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D%2A%28+t%5B1%5D+%2B+24+%29%2A%28+t%5B1%5D+-+8+%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=+%28+t%5B1%5D+%2B+24+%29%2A%28+t%5B1%5D+-+8+%29+%2B+t%5B1%5D%2A%28+t%5B1%5D+-+8+%29+=+t%5B1%5D%2A%28+t%5B1%5D+%2B+24+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D%5E2+%2B+24t%5B1%5D+-+8t%5B1%5D+-+192+%2B+t%5B1%5D%5E2+-+8t%5B1%5D+=+t%5B1%5D%5E2+%2B+24t%5B1%5D+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D%5E2+-+16t%5B1%5D++=+192+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D%5E2+-+16t%5B1%5D++=+192+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Complete the square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++t%5B1%5D%5E2+-+16t%5B1%5D+%2B+%2816%2F2%29%5E2+=+192+%2B+%2816%2F2%29%5E2+ ALIGN=MIDDLE  ALT=\"++t%5B1%5D%5E2+-+16t%5B1%5D+%2B+%2816%2F2%29%5E2+=+192+%2B+%2816%2F2%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++t%5B1%5D%5E2+-+16t%5B1%5D+%2B+64+=+192+%2B+64+ ALIGN=MIDDLE  ALT=\"++t%5B1%5D%5E2+-+16t%5B1%5D+%2B+64+=+192+%2B+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+t%5B1%5D+-+8+%29%5E2+=+256+ ALIGN=MIDDLE  ALT=\"+%28+t%5B1%5D+-+8+%29%5E2+=+256+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+t%5B1%5D+-+8+%29%5E2+=+16%5E2+ ALIGN=MIDDLE  ALT=\"+%28+t%5B1%5D+-+8+%29%5E2+=+16%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+-+8+=+16+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+-+8+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+=+24+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+=+24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The larger pipe takes 24 min filling alone<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Ft%5B1%5D+%2B+1%2F%28+t%5B1%5D+%2B+24+%29+=+1%2F%28+t%5B1%5D+-+8+%29+ ALIGN=MIDDLE  ALT=\"+1%2Ft%5B1%5D+%2B+1%2F%28+t%5B1%5D+%2B+24+%29+=+1%2F%28+t%5B1%5D+-+8+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F24+%2B+1%2F%28+24+%2B+24+%29+=+1%2F%28+24+-+8+%29+ ALIGN=MIDDLE  ALT=\"+1%2F24+%2B+1%2F%28+24+%2B+24+%29+=+1%2F%28+24+-+8+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F24+%2B+1%2F48+=+1%2F16+ ALIGN=MIDDLE  ALT=\"+1%2F24+%2B+1%2F48+=+1%2F16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F48+%2B+1%2F48+=+3%2F48+ ALIGN=MIDDLE  ALT=\"+2%2F48+%2B+1%2F48+=+3%2F48+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F48+=+3%2F48+ ALIGN=MIDDLE  ALT=\"+3%2F48+=+3%2F48+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );