document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=807710>Question 807710</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If three pipes are all opened, they can fill an empty swimming pool in 3 hours. The largest pipe alone takes 1/3 the time that the smallest pipe takes and half the time the other pipe takes. How long would it take each pipe to fill the pool by itself? <BR>\n" );
document.write( " Can you be a little specific because i'm really confused with this problem, thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #486479 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=486479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Add the rates of filling to get the rate of all 3<BR>\n" );
document.write( "pipes filling together<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;\" > = the rate of filling of the largest pipe<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;\" > = the rate of filling of the middle size pipe<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;\" > = the rate of filling of the smallest pipe<BR>\n" );
document.write( "---------------------------------------------<BR>\n" );
document.write( "If three pipes are all opened, the total rate is <BR>\n" );
document.write( "( 1 pool filled ) / ( 3 hrs ) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F3+ ALIGN=MIDDLE  ALT=\"+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B1%5D+%2B+R%5B2%5D+%2B+R%5B3%5D+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+R%5B1%5D+%2B+R%5B2%5D+%2B+R%5B3%5D+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B3%5D+=+3%2AR%5B1%5D+ ALIGN=MIDDLE  ALT=\"+R%5B3%5D+=+3%2AR%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( The largest pipe's rate is 3 times the smallest pipe )<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B3%5D+=+2%2AR%5B2%5D+ ALIGN=MIDDLE  ALT=\"+R%5B3%5D+=+2%2AR%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( The largest pipe's rate is 2 times the medium size pipe )<BR>\n" );
document.write( "--------------------------------------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B1%5D+=+%281%2F3%29%2AR%5B3%5D+ ALIGN=MIDDLE  ALT=\"+R%5B1%5D+=+%281%2F3%29%2AR%5B3%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B2%5D+=+%281%2F2%29%2AR%5B3%5D+ ALIGN=MIDDLE  ALT=\"+R%5B2%5D+=+%281%2F2%29%2AR%5B3%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Substitute these results into (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B1%5D+%2B+R%5B2%5D+%2B+R%5B3%5D+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+R%5B1%5D+%2B+R%5B2%5D+%2B+R%5B3%5D+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F3%29%2AR%5B3%5D+%2B+%281%2F2%29%2AR%5B3%5D+%2B+R%5B3%5D+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+%281%2F3%29%2AR%5B3%5D+%2B+%281%2F2%29%2AR%5B3%5D+%2B+R%5B3%5D+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B3%5D%2A%28+1%2F3+%2B+1%2F2+%2B+1+%29+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+R%5B3%5D%2A%28+1%2F3+%2B+1%2F2+%2B+1+%29+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B3%5D%2A%28+2%2F6+%2B+3%2F6+%2B+6%2F6+%29+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+R%5B3%5D%2A%28+2%2F6+%2B+3%2F6+%2B+6%2F6+%29+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2811%2F6%29%2AR%5B3%5D+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+%2811%2F6%29%2AR%5B3%5D+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B3%5D+=+%286%2F11%29%2A%282%2F6%29+ ALIGN=MIDDLE  ALT=\"+R%5B3%5D+=+%286%2F11%29%2A%282%2F6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B3%5D+=+2%2F11+ ALIGN=MIDDLE  ALT=\"+R%5B3%5D+=+2%2F11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B1%5D+=+%281%2F3%29%2AR%5B3%5D+ ALIGN=MIDDLE  ALT=\"+R%5B1%5D+=+%281%2F3%29%2AR%5B3%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B1%5D+=+%281%2F3%29%2A%282%2F11%29+ ALIGN=MIDDLE  ALT=\"+R%5B1%5D+=+%281%2F3%29%2A%282%2F11%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B1%5D+=+2%2F33+ ALIGN=MIDDLE  ALT=\"+R%5B1%5D+=+2%2F33+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B2%5D+=+%281%2F2%29%2AR%5B3%5D+ ALIGN=MIDDLE  ALT=\"+R%5B2%5D+=+%281%2F2%29%2AR%5B3%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B2%5D+=+%281%2F2%29%2A%282%2F11%29+ ALIGN=MIDDLE  ALT=\"+R%5B2%5D+=+%281%2F2%29%2A%282%2F11%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B2%5D+=+1%2F11+ ALIGN=MIDDLE  ALT=\"+R%5B2%5D+=+1%2F11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "The largest pipe can fill ( 2 pools ) / ( 33 hrs ), so<BR>\n" );
document.write( "it can fill ( 1 pool ) / ( 16.5 hrs )<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "The medium size pipe can fill ( 1 pool ) / ( 11 hrs )<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "The smallest pipe can fiill ( 2 pools ) / ( 11 hrs )<BR>\n" );
document.write( "It can fill ( 1 pool ) / ( 5.5 hrs )<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "Check the answer:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5B1%5D+%2B+R%5B2%5D+%2B+R%5B3%5D+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+R%5B1%5D+%2B+R%5B2%5D+%2B+R%5B3%5D+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F16.5+%2B+1%2F11+%2B+1%2F5.5+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+1%2F16.5+%2B+1%2F11+%2B+1%2F5.5+=+1%2F3+\"   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=+5.5+ ALIGN=MIDDLE  ALT=\"+5.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F3+%2B+1%2F2+%2B+1+=+%281%2F3%29%2A5.5+ ALIGN=MIDDLE  ALT=\"+1%2F3+%2B+1%2F2+%2B+1+=+%281%2F3%29%2A5.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F6+%2B+3%2F6+%2B+6%2F6+=+11%2F6+ ALIGN=MIDDLE  ALT=\"+2%2F6+%2B+3%2F6+%2B+6%2F6+=+11%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+11%2F6+=+11%2F6+ ALIGN=MIDDLE  ALT=\"+11%2F6+=+11%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );