document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=953872>Question 953872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Drains a, b, and c are used to empty a pool. drain a can empty the pool twice as fast as drain b. drain c can empty the pool 2 hours faster than drain a. working together, the three drains can empty the pool in 6 hours. how fast could drain b empty the pool working alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #582596 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=582596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> : Drains a, b, and c are used to empty a pool. drain a can empty the pool twice as fast as drain b. drain c can empty the pool 2 hours faster than drain a. working together, the three drains can empty the pool in 6 hours. how fast could drain b empty the pool working alone?<BR>\n" );
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document.write( "let the drain times of each be a, b, c<BR>\n" );
document.write( "write an equation for each statement<BR>\n" );
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document.write( "\" drain a can empty the pool twice as fast as drain b.\". therefore:<BR>\n" );
document.write( "b = 2a<BR>\n" );
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document.write( "\" drain c can empty the pool 2 hours faster than drain a.\" therefore:<BR>\n" );
document.write( "c =(a-2)<BR>\n" );
document.write( ":<BR>\n" );
document.write( " working together, the three drains can empty the pool in 6 hours.<BR>\n" );
document.write( "let the completed job = 1 (an empty pool)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fa ALIGN=MIDDLE  ALT=\"6%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fb ALIGN=MIDDLE  ALT=\"6%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fc ALIGN=MIDDLE  ALT=\"6%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "replace b with 2a and c with (a-2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fa ALIGN=MIDDLE  ALT=\"6%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F2a ALIGN=MIDDLE  ALT=\"6%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28%28a-2%29%29 ALIGN=MIDDLE  ALT=\"6%2F%28%28a-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "reduce the 2nd fraction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fa ALIGN=MIDDLE  ALT=\"6%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fa ALIGN=MIDDLE  ALT=\"3%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28%28a-2%29%29 ALIGN=MIDDLE  ALT=\"6%2F%28%28a-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by a(a-2), cancel the denominators and you have:<BR>\n" );
document.write( "6(a-2) + 3(a-2) + 6a = a(a-2)<BR>\n" );
document.write( "6a - 12 + 3a - 6 + 6a = a^2 - 2a<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "15a - 18 = a^2 - 2a<BR>\n" );
document.write( "Combine on the right to form a quadratic equation<BR>\n" );
document.write( "0 = a^2 - 2a - 15a + 18<BR>\n" );
document.write( "a^2 - 17a + 18 = 0<BR>\n" );
document.write( "we have to use the quadratic formula to solve this; a=1, b=-17, c=18<BR>\n" );
document.write( "I got inexact solutions, a = 15.865 is the reasonable answer<BR>\n" );
document.write( "a = 15.865 hrs alone<BR>\n" );
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document.write( " how fast could drain b empty the pool working alone?<BR>\n" );
document.write( "Takes twice as long, therefore<BR>\n" );
document.write( "2*15.865 = 31.73 hrs<BR>\n" );
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document.write( "let's check this; c=13.865 (two hrs less)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F15.865 ALIGN=MIDDLE  ALT=\"6%2F15.865\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F31.73 ALIGN=MIDDLE  ALT=\"6%2F31.73\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F13.865 ALIGN=MIDDLE  ALT=\"6%2F13.865\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( ".378 + .189 + .433 = 1, this is a good solution </SPAN>\n" );
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