document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098065>Question 1098065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A tank can be filled by a pipe in 5.0 h and emptied by another pipe in 6.0 h. How much time will be required to fill an empty tank if both are running? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #712462 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=712462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> tank can be filled in 5 hours using one pipe.<BR>\n" );
document.write( "same tank can be emptied in 6 hours using another pipe.\r<BR>\n" );
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document.write( "rate * time = quantity.\r<BR>\n" );
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document.write( "quantity equals 1 full tank.\r<BR>\n" );
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document.write( "rate * time = 1\r<BR>\n" );
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document.write( "when filing the tank, time = 5 hours, therefore rate = 1/5 of the tank in one hour.\r<BR>\n" );
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document.write( "when emptying the tank, time = 6 hours, therefore rate = 1/6 of the tank in one hour.\r<BR>\n" );
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document.write( "the filling pipe fills the tank at the rate of 1/5 of the tank in one hour.\r<BR>\n" );
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document.write( "the emptying pipe empties the tank at the rate of 1/6 of the tank in one hour.\r<BR>\n" );
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document.write( "when they are both runjning, they oppose each other, therefore the combined rate is fill rate minus the empty rate.\r<BR>\n" );
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document.write( "(1/5 - 1/6) * T = 1 is the combined equation when they are both running.\r<BR>\n" );
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document.write( "simplify by placing the fractions under the saem denominator to get:\r<BR>\n" );
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document.write( "(6/30 - 5/30) * T = 1\r<BR>\n" );
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document.write( "combined rate becomes 1/30, therefore 1/30 * T = 1\r<BR>\n" );
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document.write( "solve for T to get T = 30 hours.\r<BR>\n" );
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document.write( "it would take 30 hours to fill the tank if both the filling pipe and the emptying pipe are tunning at the same time.\r<BR>\n" );
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document.write( "in 30 hours, the amount of water poured into the tank is equal to 1/5 * 30 = 6 times the capacity of the tank.\r<BR>\n" );
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document.write( "in 30 hours, the amount of water empties out of the tank is equal to 1/6 * 30 = 5 times the capacity of the tank.\r<BR>\n" );
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document.write( "you are left with the capacity of the tank which is 1 full tank.\r<BR>\n" );
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document.write( "to place this into gallons of water, assume 1 full tank is equal to 600 gallons.\r<BR>\n" );
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document.write( "the tank is filled in 5 hours, therefore rate * time = quantity becomes rate * 5 = 600 and you get a fill rate of 120 gallons per hour.\r<BR>\n" );
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document.write( "the tank is emptied in 6 hours, therefore rate * time = quantity becomes rate * 6 = 600 and you get an empty rate of 100 gallons per hour.\r<BR>\n" );
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document.write( "when both pipes are turned on at the same time, you get a fill rate of 120 gallons per hour and an empty rate of 100 gallons per hour which give you a net fill rate of 20 gallons per hour.\r<BR>\n" );
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document.write( "at 20 gallons per hour net fill rate, it will take 30 hours to fill the tank to 600 gallon capacity.\r<BR>\n" );
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document.write( "you get the same answer except we're using 600 gallons as the quantity rather than 1 full tank as quantity.\r<BR>\n" );
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