document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=498554>Question 498554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pipe A can fill a pool in 5 hours.  Pipe B can fill it in 2 hours less than it takes Pipe C, a drain pipe, to empty the pool.  With all 3 pipes open it takes 3 hours to fill the pool.  How long would it take Pipe C to empty it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #337070 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=337070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a problem of rates<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > = pipe C's rate of emptying the pool<BR>\n" );
document.write( "Pipe A's rate of filling:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F5+ ALIGN=MIDDLE  ALT=\"+1%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( 1 pool in 5 hrs )<BR>\n" );
document.write( "Pipe B's rate of filling:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++1%2F%28+c+-+2%29+ ALIGN=MIDDLE  ALT=\"++1%2F%28+c+-+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Pipe C's rate of emptying pool:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------<BR>\n" );
document.write( "With all 3 pipes open:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F5+%2B+1%2F%28+c+-+2+%29+-+1%2Fc+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+1%2F5+%2B+1%2F%28+c+-+2+%29+-+1%2Fc+=+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=+15%2Ac%2A%28+c+-+2+%29+ ALIGN=MIDDLE  ALT=\"+15%2Ac%2A%28+c+-+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3c%2A%28+c+-+2+%29+%2B+15c+-+15%2A%28+c+-+2+%29+=+5c%2A%28+c+-+2+%29+ ALIGN=MIDDLE  ALT=\"+3c%2A%28+c+-+2+%29+%2B+15c+-+15%2A%28+c+-+2+%29+=+5c%2A%28+c+-+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3c%5E2+-+6c+%2B+15c+-+15c+%2B+30++=+5c%5E2+-+10c+ ALIGN=MIDDLE  ALT=\"+3c%5E2+-+6c+%2B+15c+-+15c+%2B+30++=+5c%5E2+-+10c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2c%5E2+-+4c+-+30+=+0+ ALIGN=MIDDLE  ALT=\"+2c%5E2+-+4c+-+30+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c%5E2+-+2c+-+15+=+0+ ALIGN=MIDDLE  ALT=\"+c%5E2+-+2c+-+15+=+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=+c%5E2+-+2c+%2B+%28-2%2F2%29%5E2+=+15+%2B+%28-2%2F2%29%5E2+ ALIGN=MIDDLE  ALT=\"+c%5E2+-+2c+%2B+%28-2%2F2%29%5E2+=+15+%2B+%28-2%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=+c%5E2+-+2c+%2B+1+=+16+ ALIGN=MIDDLE  ALT=\"+c%5E2+-+2c+%2B+1+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+c+-+1+%29%5E2+=+4%5E2+ ALIGN=MIDDLE  ALT=\"+%28+c+-+1+%29%5E2+=+4%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the square root of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+-+1+=+4+ ALIGN=MIDDLE  ALT=\"+c+-+1+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+5+ ALIGN=MIDDLE  ALT=\"+c+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, also<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+-+1+=+-4+ ALIGN=MIDDLE  ALT=\"+c+-+1+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-3+ ALIGN=MIDDLE  ALT=\"+c+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( can't use the negative square root )<BR>\n" );
document.write( "It will take pipe C alone 5 hours to empty pool<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F5+%2B+1%2F%28+c+-+2+%29+-+1%2Fc+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+1%2F5+%2B+1%2F%28+c+-+2+%29+-+1%2Fc+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F5+%2B+1%2F%28+5+-+2+%29+-+1%2F5+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+1%2F5+%2B+1%2F%28+5+-+2+%29+-+1%2F5+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F5+%2B+1%2F3+-+1%2F5+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+1%2F5+%2B+1%2F3+-+1%2F5+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F3+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+1%2F3+=+1%2F3+\"   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" );