document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=760966>Question 760966</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A stream flows at a rate of 4mph. A boat travels 70 miles downstream and returns in a total time of 6hr. What is the speed of the boat in still water?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463053 by </B><A HREF=/tutors/aboutme.mpl?userid=ramkikk66><B>ramkikk66(644)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ramkikk66><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=463053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A stream flows at a rate of 4mph. A boat travels 70 miles downstream and returns in a total time of 6hr. What is the speed of the boat in still water?\r<BR>\n" );
document.write( "\n" );
document.write( "Let x be the speed of boat in still water.<BR>\n" );
document.write( "Then, the speed of the boat downstream = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since it flows with the current) and speed while returning upstream = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4 ALIGN=MIDDLE  ALT=\"x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Time taken to travel 70 km downstream = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"70%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Time taken to travel 70 km upstream = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"70%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Total time = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F%28x%2B4%29+%2B+70%2F%28x-4%29+=+6 ALIGN=MIDDLE  ALT=\"70%2F%28x%2B4%29+%2B+70%2F%28x-4%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2A%28x-4%29+%2B+70%2A%28x%2B4%29+=+6%2A%28x%2B4%29%2A%28x-4%29 ALIGN=MIDDLE  ALT=\"70%2A%28x-4%29+%2B+70%2A%28x%2B4%29+=+6%2A%28x%2B4%29%2A%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140%2Ax+=+6%28x%5E2+-+16%29 ALIGN=MIDDLE  ALT=\"140%2Ax+=+6%28x%5E2+-+16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax%5E2+-+140%2Ax+-+96+=+0 ALIGN=MIDDLE  ALT=\"6%2Ax%5E2+-+140%2Ax+-+96+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > We can solve this using the standard formula for solving quadratic equations.\r<BR>\n" );
document.write( "\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=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=6x%5E2%2B-140x%2B-96+=+0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B-140x%2B-96+=+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=%28-140%29%5E2-4%2A6%2A-96=21904 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-140%29%5E2-4%2A6%2A-96=21904\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=21904 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--140%2B-sqrt%28+21904+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--140%2B-sqrt%28+21904+%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-%28-140%29%2Bsqrt%28+21904+%29%29%2F2%5C6+=+24 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-140%29%2Bsqrt%28+21904+%29%29%2F2%5C6+=+24\"   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-%28-140%29-sqrt%28+21904+%29%29%2F2%5C6+=+-0.666666666666667 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-140%29-sqrt%28+21904+%29%29%2F2%5C6+=+-0.666666666666667\"   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=6x%5E2%2B-140x%2B-96 ALIGN=MIDDLE  ALT=\"6x%5E2%2B-140x%2B-96\"   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=6x%5E2%2B-140x%2B-96+=+6%28x-24%29%2A%28x--0.666666666666667%29 ALIGN=MIDDLE  ALT=\"6x%5E2%2B-140x%2B-96+=+6%28x-24%29%2A%28x--0.666666666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 24, -0.666666666666667.\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+6%2Ax%5E2%2B-140%2Ax%2B-96+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-140%2Ax%2B-96+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The roots of the equation are x = 24, x = -0.67\r<BR>\n" );
document.write( "\n" );
document.write( "Since x cannot be negative, the speed of the boat in still water = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );