document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=415603>Question 415603</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three pipes, A, B, and C are often used two at a time to fill a tank. When A and B are used together, the tank is filled in 5 minutes. When either A and C or B and C are used together, the tank is filled in 3 minutes. How long would it take each pipe alone to fill the tank? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #291550 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=291550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Three pipes, A, B, and C are often used two at a time to fill a tank.<BR>\n" );
document.write( " When A and B are used together, the tank is filled in 5 minutes.<BR>\n" );
document.write( " When either A and C or B and C are used together, the tank is filled in 3 minutes.<BR>\n" );
document.write( " How long would it take each pipe alone to fill the tank?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let the full tank = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fa ALIGN=MIDDLE  ALT=\"5%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fb ALIGN=MIDDLE  ALT=\"5%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<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=3%2Fc ALIGN=MIDDLE  ALT=\"3%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fb ALIGN=MIDDLE  ALT=\"3%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fc ALIGN=MIDDLE  ALT=\"3%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use elimination with the 2nd and 3rd equations:<BR>\n" );
document.write( "<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=3%2Fc ALIGN=MIDDLE  ALT=\"3%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fb ALIGN=MIDDLE  ALT=\"3%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fc ALIGN=MIDDLE  ALT=\"3%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "-----------------------------Subtraction eliminates 3/c<BR>\n" );
document.write( "<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=3%2Fb ALIGN=MIDDLE  ALT=\"3%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "<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=3%2Fb ALIGN=MIDDLE  ALT=\"3%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "a = b<BR>\n" );
document.write( ":<BR>\n" );
document.write( "using the 1st equation, replace b with a<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fa ALIGN=MIDDLE  ALT=\"5%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fa ALIGN=MIDDLE  ALT=\"5%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fa ALIGN=MIDDLE  ALT=\"10%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "a = 10 hrs alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "b = 10 hrs alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find c:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F10 ALIGN=MIDDLE  ALT=\"3%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fc ALIGN=MIDDLE  ALT=\"3%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by 10c<BR>\n" );
document.write( "3c + 10(3) = 10c<BR>\n" );
document.write( "30 = 10c - 3c<BR>\n" );
document.write( "30 = 7c<BR>\n" );
document.write( "c = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F7 ALIGN=MIDDLE  ALT=\"30%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c = 4<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F7 ALIGN=MIDDLE  ALT=\"2%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Summarize: A = 10 hrs, B = 10 hrs, C = 4<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F7 ALIGN=MIDDLE  ALT=\"2%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can check this in the original equations using; C=4.2857<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );