document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163885>Question 1163885</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pump A can fill a tank in 6 hours. Pump B can empty<BR>\n" );
document.write( "the same tank in 10 hours. How long will it take both<BR>\n" );
document.write( "pumps working together to fill the tank? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788117 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=788117\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A fills the tank in 6 hours<BR>\n" );
document.write( "B empties the tank in 10 hours.\r<BR>\n" );
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document.write( "rate * time = quantity<BR>\n" );
document.write( "time is in hours.<BR>\n" );
document.write( "quantity is 1 tank<BR>\n" );
document.write( "rate = quantity divided by time.\r<BR>\n" );
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document.write( "for pump A, the formula becomes rate * 6 = 1.<BR>\n" );
document.write( "solve for rate to get pump A rate = 1/6 of the tank is filled each hour.\r<BR>\n" );
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document.write( "for pump B, the formula gecomew rate * 10 = 1.<BR>\n" );
document.write( "solve for rate to get pump B rate = 1/10 of the tank is emptied each hour.\r<BR>\n" );
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document.write( "when one pump is working to fill the tank and one pump is working to empty the tank, their rates are subtractive.\r<BR>\n" );
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document.write( "if they were both working together to fill the tank, their rates would be additive.\r<BR>\n" );
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document.write( "the formula is  therefore (rate A minus rate B) * time = 1<BR>\n" );
document.write( "this formula becomes (1/6 minus 1/10) * time = 1<BR>\n" );
document.write( "simplify to get (10/60 minus 6/60) * time = 1<BR>\n" );
document.write( "combine like terms to get 4/60 * time = 1<BR>\n" );
document.write( "solve for time to get time = 60/4 = 15 hours.\r<BR>\n" );
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document.write( "in 15 hours, pump A has filled 1/6 * 15 = 15/6 tanks.<BR>\n" );
document.write( "in 15 hours, pump B has emptied 1/10 * 15 = 15/10 tanks.<BR>\n" );
document.write( "15/6 minus 15/10 = 150/60 minus 90/60 = 60/60 = 1 tank.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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