document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184052>Question 1184052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Officials begin to release water from a full man-made lake at a rate that would empty the lake in 16 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814598 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=814598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = quantity.\r<BR>\n" );
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document.write( "you have 1 lake, so quantity = 1.\r<BR>\n" );
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document.write( "formula becomes rate * time = 1\r<BR>\n" );
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document.write( "it takes 16 weeks to empty the lake.<BR>\n" );
document.write( "rate * 16 = 1<BR>\n" );
document.write( "rate = 1/16<BR>\n" );
document.write( "this means 1/16 of the lake is empties each week.\r<BR>\n" );
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document.write( "it takes 25 weeks to fill up the lake.<BR>\n" );
document.write( "rate * 25 = 1<BR>\n" );
document.write( "rate = 1/25<BR>\n" );
document.write( "this means 1/25 of the lake is replenished each week.\r<BR>\n" );
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document.write( "every week, 1/16 week of the lake is removed and 1/25 of the lake is replenished.<BR>\n" );
document.write( "the net loss each week is 1/16 - 1/25 = 25/400 - 16/400 = 9/400 of the lake.\r<BR>\n" );
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document.write( "if you start with a full lake and have a net loss of 9/400 of the lake each week, the formula of rate * time = quantity becomes 9/400 * time = 1<BR>\n" );
document.write( "solve for time to get:<BR>\n" );
document.write( "time = 400/9 weeks.\r<BR>\n" );
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document.write( "the lake will be empty in 400/9 weeks.\r<BR>\n" );
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document.write( "in that time, the amount of lake that is removed is 1/16 * 400/9 = 25/9 times the original amount of the lake.\r<BR>\n" );
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document.write( "in that time, the amount of lake that is replenished is 1/25 * 400/9 = 16/9 times the original amount of the lake.\r<BR>\n" );
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document.write( "the net amount of lake that is removed in 400/9 weeks is 25/9 - 16/9 = 9/9 = 1 times the mount of water in the lake.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "the solution is that it takes 400/9 weeks to empty the lake.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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