document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170889>Question 170889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Each valve A, B, and C, when open, releases water into a tank at its own constant rate. With all three valves open, the tank fills in 1 hour, with only valves A and C open it takes 1.5 hours, and with only valves B and C open it takes 2 hours. How many hours will it take to fill the tank with only valves A and B open? \r<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 #126167 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each valve A, B, and C, when open, releases water into a tank at its own constant rate. With all three valves open, the tank fills in 1 hour, with only valves A and C open it takes 1.5 hours, and with only valves B and C open it takes 2 hours. How many hours will it take to fill the tank with only valves A and B open? <BR>\n" );
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document.write( "time * rate = work done<BR>\n" );
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document.write( "1(1/a + 1/b + 1/c) = 1<BR>\n" );
document.write( "(3/2)(1/a + 1/c) = 1<BR>\n" );
document.write( "2(1/b + 1/c) = 1<BR>\n" );
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document.write( "      1/a    + 1/b     + 1/c        = 1<BR>\n" );
document.write( "(3/2)(1/a)  + 0        + (3/2)(1/c) = 1<BR>\n" );
document.write( "       0    + (2)(1/b) + (2)(1/c)   = 1<BR>\n" );
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document.write( "Use any method you know to solve this system to get:<BR>\n" );
document.write( "1/a = 1/2<BR>\n" );
document.write( "1/b = 1/3<BR>\n" );
document.write( "1/c = 1/6<BR>\n" );
document.write( "Comment: These are the rates at which each will fill do the job.<BR>\n" );
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document.write( "A will take 2 hrs<BR>\n" );
document.write( "B will take 3 hrs.<BR>\n" );
document.write( "C will take 6 hours<BR>\n" );
document.write( "Comment: These are the times each will take to do the job.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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