document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=532541>Question 532541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Both inlet and outlet pipes to a cider barrel were mistakenly left open. Nevertheless, the barrel filled in 12 hours. With only the outlet pipe open, a full barrel of cider can be emptied in 1 hour more than the time to fill an empty barrle with only the inlet pipe open. How long would draining a full barrel of cider take with the outlet pipe open and the inlet pipe closed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350863 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=350863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Both inlet and outlet pipes to a cider barrel were mistakenly left open.<BR>\n" );
document.write( " Nevertheless, the barrel filled in 12 hours.<BR>\n" );
document.write( " With only the outlet pipe open, a full barrel of cider can be emptied in 1 hour more than the time to fill an empty barrel with only the inlet pipe open.<BR>\n" );
document.write( " How long would draining a full barrel of cider take with the outlet pipe open and the inlet pipe closed?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let t = time required by the outlet pipe with inlet closed, to drain the barrel<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t-1) = time required by the inlet pipe to fill the barrel (outlet closed)<BR>\n" );
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document.write( "let a full tank = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28t-1%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28t-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Ft ALIGN=MIDDLE  ALT=\"12%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by t(t-1) to clear the denominators, results:<BR>\n" );
document.write( "12t - 12(t-1) = t(t-1)<BR>\n" );
document.write( "12t - 12t + 12 = t^2 - t<BR>\n" );
document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "0 = t^2 - t - 12<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(t-4)(t+3) = 0<BR>\n" );
document.write( "the positive solution is all we want here<BR>\n" );
document.write( "t = 4 hrs to drain the tank with the inlet closed<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F3 ALIGN=MIDDLE  ALT=\"12%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F4 ALIGN=MIDDLE  ALT=\"12%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "4 - 3 = 1 </SPAN>\n" );
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