document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161585>Question 161585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A river is flowing at a rate of 5 km/h. A boat travels 12km upstream and 36km downstream in a total of 9hours. What is the speed of the boat in still water? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119061 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=119061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A river is flowing at a rate of 5 km/h. A boat travels 12km upstream and 36km downstream in a total of 9hours. What is the speed of the boat in still water?<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "B = speed of boat<BR>\n" );
document.write( "B-5 = speed of boat upstream<BR>\n" );
document.write( "B+5 = speed downstream<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "h = hours going upstream<BR>\n" );
document.write( "h*(B-5) = 12<BR>\n" );
document.write( "(9-h)*(B+5) = 36<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "B = 12/h + 5<BR>\n" );
document.write( "B = 36/(9-h) - 5<BR>\n" );
document.write( "B = 12/h + 5 = 36/(9-h) - 5<BR>\n" );
document.write( "12/h + 10 = 36/(9-h)<BR>\n" );
document.write( "Multiply by h*(9-h)<BR>\n" );
document.write( "12(9-h) + 10h(9-h) = 36h<BR>\n" );
document.write( "108-12h + 90h-10h^2 = 36h<BR>\n" );
document.write( "Collect terms<BR>\n" );
document.write( "-10h^2 + 42h + 108 = 0<BR>\n" );
document.write( "5h^2 - 21h - 54 = 0<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=5x%5E2%2B-21x%2B-54+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B-21x%2B-54+=+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=%28-21%29%5E2-4%2A5%2A-54=1521 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-21%29%5E2-4%2A5%2A-54=1521\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1521 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--21%2B-sqrt%28+1521+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--21%2B-sqrt%28+1521+%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-%28-21%29%2Bsqrt%28+1521+%29%29%2F2%5C5+=+6 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-21%29%2Bsqrt%28+1521+%29%29%2F2%5C5+=+6\"   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-%28-21%29-sqrt%28+1521+%29%29%2F2%5C5+=+-1.8 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-21%29-sqrt%28+1521+%29%29%2F2%5C5+=+-1.8\"   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=5x%5E2%2B-21x%2B-54 ALIGN=MIDDLE  ALT=\"5x%5E2%2B-21x%2B-54\"   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=5x%5E2%2B-21x%2B-54+=+%28x-6%29%2A%28x--1.8%29 ALIGN=MIDDLE  ALT=\"5x%5E2%2B-21x%2B-54+=+%28x-6%29%2A%28x--1.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6, -1.8.\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+5%2Ax%5E2%2B-21%2Ax%2B-54+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-21%2Ax%2B-54+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "The online solver always uses x, so sub h for x.<BR>\n" );
document.write( "The -1.8 hours is not usable, so the time going upstream is,<BR>\n" );
document.write( "h = 6 hours.<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Sub h into B = 12/h + 5 to solve for B<BR>\n" );
document.write( "B = 12/6 + 5<BR>\n" );
document.write( "B = 7 kph<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "The people should have gotten out and walked, woulda been faster.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );