document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185242>Question 1185242</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A cistern can be filled by two pipes. The small pipe alone will take 24 minutes <BR>\n" );
document.write( "longer than the larger pipe to fill the cistern alone. The small pipe alone will take <BR>\n" );
document.write( "32 minutes longer to fill the cistern alone than when the two pipes are operating <BR>\n" );
document.write( "together. How long will it take the larger pipe to fill the cistern alone. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816072 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=816072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A cistern can be filled by two pipes.<BR>\n" );
document.write( " let x = time required by the larger pipe alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( " The small pipe alone will take 24 minutes longer than the larger pipe to fill the cistern alone.<BR>\n" );
document.write( " (x+24) = time required by the smaller pipe<BR>\n" );
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document.write( " The small pipe alone will take 32 minutes longer to fill the cistern alone than when the two pipes are operating together.<BR>\n" );
document.write( "let t = time required when working together<BR>\n" );
document.write( "then<BR>\n" );
document.write( "t + 32 = x+24<BR>\n" );
document.write( "t = x + 24 - 32<BR>\n" );
document.write( "t = x - 8, time required when working together<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let the full cistern = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-8%29%2Fx ALIGN=MIDDLE  ALT=\"%28x-8%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-8%29%2F%28x%2B24%29 ALIGN=MIDDLE  ALT=\"%28x-8%29%2F%28x%2B24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by x(x+24)<BR>\n" );
document.write( "(x+24)(x-8) +  x(x-8) = x(x+24)<BR>\n" );
document.write( "x^2 - 8x + 24x - 192 + x^2 - 8x = x^2 + 24x<BR>\n" );
document.write( "Combine like terms on the left<BR>\n" );
document.write( "x^2 + x^2 - x^2 - 8x + 24x - 8x - 24x - 192 = 0<BR>\n" );
document.write( "x^2 - 16x - 192 = 0<BR>\n" );
document.write( "a quadratic equation which we can factor<BR>\n" );
document.write( "(x-24)(x+8) = 0<BR>\n" );
document.write( "positive solution<BR>\n" );
document.write( "x = 24 min, large pipe working alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution<BR>\n" );
document.write( "small pipe alone: 24 + 24 = 48 min<BR>\n" );
document.write( "working together: 24 - 8 = 16 min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F24 ALIGN=MIDDLE  ALT=\"16%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F48 ALIGN=MIDDLE  ALT=\"16%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );