document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003410>Question 1003410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small pipe can fill a tank in 8 min more time than it takes a larger pipe to fill the same tank. Working together, the pipes can fill the tank in 3 min. How long would it take each pipe, working alone, to fill the tank?\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 #620202 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=620202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A small pipe can fill a tank in 8 min more time than it takes a larger pipe to fill the same tank.<BR>\n" );
document.write( " Working together, the pipes can fill the tank in 3 min.<BR>\n" );
document.write( " How long would it take each pipe, working alone, to fill the tank? <BR>\n" );
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document.write( "let t = time for the larger pipe to fill the tank alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t+8) = time for the smaller pipe to do it<BR>\n" );
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document.write( "let the completed job = 1 (a full tank)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ft ALIGN=MIDDLE  ALT=\"3%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%28%28t%2B8%29%29 ALIGN=MIDDLE  ALT=\"3%2F%28%28t%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by t(t+8), cancel the denominators and you have<BR>\n" );
document.write( "3(t+8) + 3t = t(t+8)<BR>\n" );
document.write( "3t + 24 + 3t = t^2 + 8t<BR>\n" );
document.write( "Combine like terms on the right<BR>\n" );
document.write( "0 = t^2 + 8t - 6t - 24<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "t^2 + 2t - 24 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(t+6)(t-4) = 0<BR>\n" );
document.write( "We only want the positive solution here<BR>\n" );
document.write( "t = 4 min for the larger pipe to fill the tank<BR>\n" );
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document.write( "Check solution (small pipe requires 12 min)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F12 ALIGN=MIDDLE  ALT=\"3%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1\r<BR>\n" );
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