document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136098>Question 136098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kurt rows 72 km upstream and 72km back in a total of 7hrs. The speed of the river is 3km/h. Find kurt's speed 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 #99683 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99683\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let s=Kurt's speed in still water.<BR>\n" );
document.write( "d=st<BR>\n" );
document.write( "s-3=speed upstream<BR>\n" );
document.write( "s+3=speed downstream<BR>\n" );
document.write( "t=time upstream<BR>\n" );
document.write( "7-t=time downstream<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A) t(s-3)=72 upstream<BR>\n" );
document.write( "B) <BR>\n" );
document.write( "-(t-7)(s+3)=72 Downstream<BR>\n" );
document.write( "-ts+7s-3t+21=72<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A) t=72/(s-3)<BR>\n" );
document.write( "B) <BR>\n" );
document.write( "-72/(s-3) * s + 7s - 3*72/(s-3)=72-21 replace t with 72/(s-3)<BR>\n" );
document.write( "-72s/(s-3) + 7s - 216/(s-3)=51<BR>\n" );
document.write( "-72s+7s(s-3)-216=51(s-3) multiply each side by s-3 to eliminate fractions.<BR>\n" );
document.write( "-72s+7s^2-21s-216=51s-153<BR>\n" );
document.write( "-72s+7s^2-21s-216-51s+153=0<BR>\n" );
document.write( "7s^2-144s-63=0<BR>\n" );
document.write( "s=21 kph (see below)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "t=72/21-3=72/18=4h upstream<BR>\n" );
document.write( "7-4=3h downstream<BR>\n" );
document.write( "18*4=72<BR>\n" );
document.write( "24*3=72<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed<BR>\n" );
document.write( ".<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=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=7x%5E2%2B-144x%2B-63+=+0 ALIGN=MIDDLE  ALT=\"7x%5E2%2B-144x%2B-63+=+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=%28-144%29%5E2-4%2A7%2A-63=22500 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-144%29%5E2-4%2A7%2A-63=22500\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=22500 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--144%2B-sqrt%28+22500+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--144%2B-sqrt%28+22500+%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-%28-144%29%2Bsqrt%28+22500+%29%29%2F2%5C7+=+21 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-144%29%2Bsqrt%28+22500+%29%29%2F2%5C7+=+21\"   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-%28-144%29-sqrt%28+22500+%29%29%2F2%5C7+=+-0.428571428571429 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-144%29-sqrt%28+22500+%29%29%2F2%5C7+=+-0.428571428571429\"   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=7x%5E2%2B-144x%2B-63 ALIGN=MIDDLE  ALT=\"7x%5E2%2B-144x%2B-63\"   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=7x%5E2%2B-144x%2B-63+=+%28x-21%29%2A%28x--0.428571428571429%29 ALIGN=MIDDLE  ALT=\"7x%5E2%2B-144x%2B-63+=+%28x-21%29%2A%28x--0.428571428571429%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 21, -0.428571428571429.\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+7%2Ax%5E2%2B-144%2Ax%2B-63+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B-144%2Ax%2B-63+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );