document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196788>Question 196788</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A faucet can deliver water rapidly than a drain can remove it. IF the sink is empty, the drain and the faucet is opened then the sink fills in 4 minutes. The drain is able to empty a full sink in 2 minutes longer than the faucet can fill the sink when the drain is closed. What are the tines needed far each to fill or drain if it works alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147510 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=147510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <b><i>t</i></b> represent the number of minutes required for the faucet to fill the sink with the drain closed.  Then <b><i>t</i> + 2</b> represents the number of minutes it takes the drain to empty a full sink.  Then the faucet can fill <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{t}\"> of the sink in 1 minute, and the drain can empty <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  \frac {1}{t + 2}\"> of the sink in 1 minute, and working together they fill <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  \frac{1}{4}\"> of the sink in 1 minute.\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{t} - \frac{1}{t + 2} = \frac{1}{4}\">\r<BR>\n" );
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document.write( "LCD is the product of the denominators: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 4t^2 + 8t\">, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{4t+8-4t}{4t^2 - 8t}=\frac{t^2 + 2t}{4t^2+8t}\">\r<BR>\n" );
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document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 4t^2 + 8t\"> and collect terms on the left:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t^2 + 2t - 8 = 0\">\r<BR>\n" );
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document.write( "Solve the quadratic, excluding the negative root (the sink certainly didn't fill before you turned the water on) to get the time it takes the faucet to fill the sink.  Add 2 to get the time for the drain.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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