document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=77794>Question 77794</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A regular tank can be filled with water by two pipes (one larger, one smaller) in 11 1/9 mins. If the larger pipe alone takes 5 mins less to fill the tank than the smaller pipe, find the time each pipe takes to fill the tank?\r<BR>\n" );
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document.write( "p/s: I know the answer can be evaluated uses this equation,\r<BR>\n" );
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document.write( "1/x + 1/(x-5) = 1/(11 1/9) \r<BR>\n" );
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document.write( "x (smaller tank) = Ans, x-5 (larger tank) = Ans\r<BR>\n" );
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document.write( "where x is the amount of time required for the smaller tank alone to fill the tank.\r<BR>\n" );
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document.write( "BUT, \r<BR>\n" );
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document.write( "1)WHY do you use the reciprocal of each to derive at the equation?<BR>\n" );
document.write( "2)What is the concept behind the equation here? Has it got to do with the definition of reciprocals? or do we solve it using ratio? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55792 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=55792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> RATE--- IS THE CONCEPT BEHIND THE EQUATION\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "Pipe 1 alone fills a tank in 10 min<BR>\n" );
document.write( "Pipe 2 alone fills the tank in 20 min\r<BR>\n" );
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document.write( "If both are turned on together, how long will it take to fill the tank???\r<BR>\n" );
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document.write( "Pipe 1 fills at the RATE of 1/10th tank per min<BR>\n" );
document.write( "Pipe 2 fills at the RATE of 1/20th tank per min\r<BR>\n" );
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document.write( "Pipe 1  +  Pipe 2 fills at the rate of 1/10+1/20 or 3/20th tank per min\r<BR>\n" );
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document.write( "Let x= time to fill the tank<BR>\n" );
document.write( "(3/20)(x)=1  Where 1 denotes a full tank (Multiply both sides by 20)<BR>\n" );
document.write( "3x=20<BR>\n" );
document.write( "x=6 2/3 min----------both working together\r<BR>\n" );
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document.write( "NOW YOUR PROBLEM<BR>\n" );
document.write( "Let x= amount of time for smaller pipe to fill the tank\r<BR>\n" );
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document.write( "Then (x-5)=amount of time for larger pipe to fill the tank\r<BR>\n" );
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document.write( "NOW HERE'S WHERE THE RECIPROCAL COMES IN:\r<BR>\n" );
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document.write( "The smaller pipe fills the tank at the RATE of 1/x cu units per min \r<BR>\n" );
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document.write( "The larger tank fills the tank at the RATE of 1/(x-5) cu units per min\r<BR>\n" );
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document.write( "Together, they fill the tank at the rate of 1/x+(1/(x-5)) cu units per min\r<BR>\n" );
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document.write( "But now we are told that together the fill the tank in 11 1/9 minutes. so our equation to solve is:\r<BR>\n" );
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document.write( "(1/x+(1/(x-5))(11 1/9)=1   where 1 denotes a full tank.  In fact, in each of the above reciprocals, the 1 denotes a full tank.\r<BR>\n" );
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document.write( "So, dividing both sides by 11 1/9, we get:\r<BR>\n" );
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document.write( "1/x+(1/(x-5)=1/(11 1/9)--------------  which is your equation<BR>\n" );
document.write( "I assume that you have no problems solviing this eq.\r<BR>\n" );
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document.write( "Hope this helps----ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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