document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=311523>Question 311523</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you solve a problem like this:<BR>\n" );
document.write( "One pipe can fill a reservoir 1 hr faster than another pipe. Together they can fill the reservoir in 4 hrs. How long to the nearest tenth of an hour does it take the faster pipe to fill the reservoir by itself? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #222819 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=222819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One pipe can fill a reservoir 1 hr faster than another pipe. Together they can fill the reservoir in 4 hrs. How long to the nearest tenth of an hour does it take the faster pipe to fill the reservoir by itself?<BR>\n" );
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document.write( "Let x = rate of slower pipe<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x-1 = rate of faster pipe<BR>\n" );
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document.write( "4(1/x + 1/(x-1)) = 1<BR>\n" );
document.write( "4((x-1) + x) = x(x-1)<BR>\n" );
document.write( "4(2x-1) = x(x-1)<BR>\n" );
document.write( "8x-4 = x^2-x<BR>\n" );
document.write( "-4 = x^2-9x<BR>\n" );
document.write( "0 = x^2-9x+4<BR>\n" );
document.write( "Because we can't factor, we must resort to the quadratic formula.  Doing so yields:<BR>\n" );
document.write( "x = {0.5, 8.5}<BR>\n" );
document.write( "Tossing out the 0.5 (because calculating the faster pipe will produce a negative answer) leaves:<BR>\n" );
document.write( "x = 8.5 hrs<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Time for faster pipe to fill: 8.5-1 = 7.5 hours<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic follows:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-9x%2B4+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-9x%2B4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-9%29%5E2-4%2A1%2A4=65 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-9%29%5E2-4%2A1%2A4=65\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=65 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--9%2B-sqrt%28+65+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--9%2B-sqrt%28+65+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+65+%29%29%2F2%5C1+=+8.53112887414927 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+65+%29%29%2F2%5C1+=+8.53112887414927\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-9%29-sqrt%28+65+%29%29%2F2%5C1+=+0.468871125850725 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-9%29-sqrt%28+65+%29%29%2F2%5C1+=+0.468871125850725\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-9x%2B4 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-9x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-9x%2B4+=+1%28x-8.53112887414927%29%2A%28x-0.468871125850725%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-9x%2B4+=+1%28x-8.53112887414927%29%2A%28x-0.468871125850725%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 8.53112887414927, 0.468871125850725.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-9%2Ax%2B4+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-9%2Ax%2B4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );