document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=960284>Question 960284</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a garden hose takes 180 minutes to fill up a hot tub, whereas it takes 300 minutes to drain it, if the drain is accidentally left open how long will it take to fill the hot tub? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #586857 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=586857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate of filling is 1/180 of the tub in one minute.<BR>\n" );
document.write( "rate of emptying is 1/300 of the tub in one minute.\r<BR>\n" );
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document.write( "rate * time = quantity.<BR>\n" );
document.write( "quantity is 1 full tub.<BR>\n" );
document.write( "rate of filling and emptying work against each other, so their rates are subtractive.<BR>\n" );
document.write( "time is what you want to find.\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "(1/180 - 1/300) * T = 1<BR>\n" );
document.write( "multiply both sides of this equation by 180 * 300 and you get:\r<BR>\n" );
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document.write( "(300 - 180) * T = 180 * 300\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "120 * T = 180 * 300\r<BR>\n" );
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document.write( "divide both sides of this equation by 120 to get:\r<BR>\n" );
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document.write( "T = 180 * 300 / 120\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "T = 450 minutes.\r<BR>\n" );
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document.write( "in 450 minutes, 450/180 = 2.5 times the tub has been filled and 450 / 300 = 1.5 times the tub has been emptied resulting in 1 full tub.\r<BR>\n" );
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document.write( "every minute 1/180 of the tub is being filled and 1/300 of the tub is being empties, result in a net fill of 1/450 of the tub being filled.\r<BR>\n" );
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document.write( "at that rate, the tub will be filled in 450 minutes.\r<BR>\n" );
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document.write( "the solution checks out.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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