document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896484>Question 896484</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two taps A & B altogether fill a swimming pool in 15 hrs. Taps A & B are kept open for 12 hrs & then Tap B is closed. It takes another 8 hrs for the swimming pool to be filled. How many hours does each tap requires to fill the swimming pool. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543537 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=543537\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let A equal the rate of tap A.<BR>\n" );
document.write( "let B equal the rate of tap B.\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( "the formula to use is R*T = Q\r<BR>\n" );
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document.write( "Q = 1 which represents 1 full pool.\r<BR>\n" );
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document.write( "T = 15\r<BR>\n" );
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document.write( "R = A+B\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "(A+B)*15 = 1\r<BR>\n" );
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document.write( "you can solve for (A+B) to get:\r<BR>\n" );
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document.write( "(A+B) = 1/15\r<BR>\n" );
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document.write( "that's the combined rate when both pipes are open.\r<BR>\n" );
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document.write( "now you run both pipes for 12 hours.\r<BR>\n" );
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document.write( "since R*T = Q, your formula becomes:\r<BR>\n" );
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document.write( "(A+B)*12 = x\r<BR>\n" );
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document.write( "Q is equal to x because we don't know what it is yet.\r<BR>\n" );
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document.write( "but we do know that (A+B) = 1/15, so we get:\r<BR>\n" );
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document.write( "1/15 * 12 = x which results in x = 12/15 which can be simplified to x = 4/5.\r<BR>\n" );
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document.write( "the both pipes can fill 4/5 of the pool in 12 hours.\r<BR>\n" );
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document.write( "that leaves 1/5 of the pool still needing to be filled.\r<BR>\n" );
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document.write( "since pipe B is closed, pipe A has to finish the job.\r<BR>\n" );
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document.write( "the formula is still R*T = Q\r<BR>\n" );
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document.write( "this time Q = 1/5 and T = 8 and R = A only because B is closed.\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "8*A = 1/5\r<BR>\n" );
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document.write( "solve for A to get A = 1/40\r<BR>\n" );
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document.write( "that's the rate of pipe A.\r<BR>\n" );
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document.write( "pipe A can fill 1/40 of the pool in one hour.\r<BR>\n" );
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document.write( "now we want to know the rate of pipe B.\r<BR>\n" );
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document.write( "since we know that A+B = 1/15 and we know that A = 1/40, we can substitute in this equation to find B.\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "1/40 + B = 1/15\r<BR>\n" );
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document.write( "subtract 1/40 from both sides of this equation to get:\r<BR>\n" );
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document.write( "B = 1/15 - 1/40 which is equivalent to:\r<BR>\n" );
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document.write( "B = 8/120 - 3/120 which is equal to 5/120 which is equal to 1/24.\r<BR>\n" );
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document.write( "we now have the individual rates.\r<BR>\n" );
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document.write( "A = 1/40<BR>\n" );
document.write( "B = 1/24\r<BR>\n" );
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document.write( "pipe A will take 40 hours to fill the pool by itself.<BR>\n" );
document.write( "pipe B will take 24 hours to fill the pool by itself.\r<BR>\n" );
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document.write( "working together, the formula becomes (A+B)*15 = 1\r<BR>\n" );
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document.write( "replace A and B with their respective values and you get:\r<BR>\n" );
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document.write( "(1/40 + 1/24) * 15 = 1\r<BR>\n" );
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document.write( "solve to get:\r<BR>\n" );
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document.write( "1 = 1 which confirms the solutions are good.\r<BR>\n" );
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document.write( "12 hours working together fills 4/5 of the pool and then pipe A takes over for the remaining 1/5 of  the pool working at 1/40 of the pool per hour.\r<BR>\n" );
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document.write( "1/40 * 8 = 8/40 = 1/5.\r<BR>\n" );
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document.write( "solution is confirmed.\r<BR>\n" );
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document.write( "rates are:\r<BR>\n" );
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document.write( "A = 1/40 of the pool per hour.<BR>\n" );
document.write( "B = 1/24 of the pool per hour.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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