document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1064379>Question 1064379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two pipes running simultaneously can fill a swimming pool in 6 hours. If both pipes run for 3 hours and the first is then shut-off, it requires 4 hours more for the second to fill the pool. How long does it take the pipe to fill the tank if the drain is closed?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #679428 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=679428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x is the rate of the first pipe.<BR>\n" );
document.write( "y is the rate of the second pipe.\r<BR>\n" );
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document.write( "rate * time = quantity of work produced.\r<BR>\n" );
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document.write( "when they work together their rates are additive\r<BR>\n" );
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document.write( "therefore, (x + y) * 6 = 1\r<BR>\n" );
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document.write( "simplify this to get 6x + 6y = 1\r<BR>\n" );
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document.write( "when they both work for 3 hours, they fill 1/2 the pool.\r<BR>\n" );
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document.write( "one of them is then shut shut and the other takes 4 hours to fill the pool.\r<BR>\n" );
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document.write( "assuming the rate of the pipe that fills half the pool in 4 hours is x, then you get:\r<BR>\n" );
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document.write( "4x = 1/2\r<BR>\n" );
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document.write( "this says that the second pipe, working at a rate of x amount of the pool in one hour, takes 4 hours to fill half the pool.\r<BR>\n" );
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document.write( "if you multiply both sides of that equation by 2, you will see that the second pipe takes 8 hours to fill the pool by itself.\r<BR>\n" );
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document.write( "to find out how long it takes the first pipe to fikll the pool by itself, you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "6x + 6y = 1<BR>\n" );
document.write( "4x = 1/2\r<BR>\n" );
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document.write( "solve for x to get x = 1/8.\r<BR>\n" );
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document.write( "replace x in the first equation with 1/8 to get 6/8 + 6y = 1\r<BR>\n" );
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document.write( "simplify to get 6/8 + 6y = 8/8\r<BR>\n" );
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document.write( "subtract 6/8 from both sides of the equation to get 6y = 2/8.\r<BR>\n" );
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document.write( "solve for y to get y = (2/8)/6 = 2/48 = 1/24\r<BR>\n" );
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document.write( "the rate of the pipe that was shut off is 1/24 of the pool in one hour.\r<BR>\n" );
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document.write( "you get x = 1/8 and y = 1/24\r<BR>\n" );
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document.write( "simplify to get x = 3/24 and y = 1/24\r<BR>\n" );
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document.write( "the combined rate is 4/24 = 1/6.\r<BR>\n" );
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document.write( "go back to the original equation to get (x + y) * y = 1 which becomes 1/6 * 6 = 1 which becomes 1 = 1.\r<BR>\n" );
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document.write( "the solution is good\r<BR>\n" );
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document.write( "the rate of the pipe that was shut off after 3 hours is 1/24 of the pool in one hour.<BR>\n" );
document.write( "that rate was originally y that we solved to get y = 1/24.\r<BR>\n" );
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document.write( "the rate of the pipe that was left open to finish the job in 4 hours is 1/8 of the pool in one hour.<BR>\n" );
document.write( "that rate was originally x that we solved to get x = 1/8.\r<BR>\n" );
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