document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320359>Question 320359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At first two different pipes running together will fill a tank in 20/3 minutes. The rate that water runs through each of the pipes is then adjusted. If one pipe, running alone, takes 1 minute less to fill the tank at its new rate, and the other pipe, running alone, takes 2 minutes more to fill the tank at its new rate, then the two running together will fill the tank in 7 minutes. Find in what time the tank will be filled by each pipe running alone at the new rates. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229563 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=229563\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At first two different pipes running together will fill a tank in 20/3 minutes.<BR>\n" );
document.write( " The rate that water runs through each of the pipes is then adjusted.<BR>\n" );
document.write( " If one pipe, running alone, takes 1 minute less to fill the tank at its new <BR>\n" );
document.write( "rate,<BR>\n" );
document.write( " and the other pipe, running alone, takes 2 minutes more to fill the tank<BR>\n" );
document.write( " at its new rate,<BR>\n" );
document.write( " then the two running together will fill the tank in 7 minutes.<BR>\n" );
document.write( ":<BR>\n" );
document.write( " Find in what time the tank will be filled by each pipe running alone at the new rates.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let a = first pipe original time alone (in minutes)<BR>\n" );
document.write( "let b = second pipe original time alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(a-1) = first pipe adjusted rate time alone<BR>\n" );
document.write( "(b+2) = 2nd pipe adjusted rate time alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let the completed job = 1 <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Original, working together equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2F3%29%2Fa ALIGN=MIDDLE  ALT=\"%2820%2F3%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2F3%29%2Fb ALIGN=MIDDLE  ALT=\"%2820%2F3%29%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "We convert this to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F%283a%29 ALIGN=MIDDLE  ALT=\"20%2F%283a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F%283b%29 ALIGN=MIDDLE  ALT=\"20%2F%283b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by 3ab, results<BR>\n" );
document.write( "20b + 20a = 3ab<BR>\n" );
document.write( "20b - 3ab = -20a<BR>\n" );
document.write( "b(20-3a) = -20a<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2820a%29%2F%2820-3a%29 ALIGN=MIDDLE  ALT=\"-%2820a%29%2F%2820-3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; use this form for substitution<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Adjusted, working together equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28a-1%29 ALIGN=MIDDLE  ALT=\"7%2F%28a-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28b%2B2%29 ALIGN=MIDDLE  ALT=\"7%2F%28b%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by (a-1)(b+2), results<BR>\n" );
document.write( "7(b+2) + 7(a-1) = (a-1)(b+2)<BR>\n" );
document.write( "7b + 14 + 7a - 7 = ab + 2a - b - 2<BR>\n" );
document.write( "Combine<BR>\n" );
document.write( "7b + b + 7a - 2a + 14 - 7 + 2 = ab<BR>\n" );
document.write( "8b + 5a + 9 = ab<BR>\n" );
document.write( "Multiply by 3, <BR>\n" );
document.write( "24b + 15a + 27 = 3ab<BR>\n" );
document.write( "The two equations = 3ab, therefore<BR>\n" );
document.write( "24b + 15a + 27 = 20b + 20a<BR>\n" );
document.write( "24b - 20b + 15a - 20a = -27<BR>\n" );
document.write( "4b - 5a = -27<BR>\n" );
document.write( "replace b with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2820a%29%2F%2820-3a%29 ALIGN=MIDDLE  ALT=\"-%2820a%29%2F%2820-3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2820a%29%2F%2820-3a%29 ALIGN=MIDDLE  ALT=\"-%2820a%29%2F%2820-3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) - 5a = -27<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2880a%29%2F%2820-3a%29 ALIGN=MIDDLE  ALT=\"-%2880a%29%2F%2820-3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 5a = -27<BR>\n" );
document.write( "Get rid of all those negatives, multiply by -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2880a%29%2F%2820-3a%29 ALIGN=MIDDLE  ALT=\"%2880a%29%2F%2820-3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 5a = 27<BR>\n" );
document.write( "Multiply by (20-3a), results<BR>\n" );
document.write( "80a + 5a(20-3a) = 27(20-3a) <BR>\n" );
document.write( "80a + 100a - 15a^2 = 540 - 81a<BR>\n" );
document.write( "180a - 15a^2 = 540 - 81a<BR>\n" );
document.write( "Combine on the right<BR>\n" );
document.write( "0 = 15a^2 - 81a - 180a + 540<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "15a^2 - 261a + 540 = 0<BR>\n" );
document.write( "Simplify, divide by 3<BR>\n" );
document.write( "5a^2 - 87a + 180 = 0<BR>\n" );
document.write( "Factor this<BR>\n" );
document.write( "(5a-12)(a-15) = 0<BR>\n" );
document.write( "Reasonable solution here<BR>\n" );
document.write( "a = 15 hrs pipe a originally<BR>\n" );
document.write( "then<BR>\n" );
document.write( "15 - 1 = 14 hrs pipe a alone at the new rate<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find b original value<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2820a%29%2F%2820-3a%29 ALIGN=MIDDLE  ALT=\"-%2820a%29%2F%2820-3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2820%2815%29%29%2F%2820-3%2815%29%29 ALIGN=MIDDLE  ALT=\"-%2820%2815%29%29%2F%2820-3%2815%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28300%29%2F%2820-45%29 ALIGN=MIDDLE  ALT=\"-%28300%29%2F%2820-45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-300%29%2F%28-25%29 ALIGN=MIDDLE  ALT=\"%28-300%29%2F%28-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = +12 hrs pipe b originally<BR>\n" );
document.write( "then<BR>\n" );
document.write( "12 + 2 = 14 hrs pipe b alone at the new rate<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution in the adjusted equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F14 ALIGN=MIDDLE  ALT=\"7%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F14 ALIGN=MIDDLE  ALT=\"7%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Seems like there should be an easier way to do this, but I see no one else has<BR>\n" );
document.write( "worked this problem in 12 hrs, so here it is.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );