document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149899>Question 149899</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321233832/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The Hudson River flows at a rate of 3 mile per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. 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 #110015 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=110015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Hudson River flows at a rate of 3 mile per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?<BR>\n" );
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document.write( "Let x = speed of patrol boat in still water<BR>\n" );
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document.write( "Time it takes to go up river:<BR>\n" );
document.write( "60/(x-3)<BR>\n" );
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document.write( "Time it takes to go down river:<BR>\n" );
document.write( "60/(x+3)<BR>\n" );
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document.write( "Therefore, we have:<BR>\n" );
document.write( "60/(x-3) + 60/(x+3) = 9<BR>\n" );
document.write( "multiplying both sides by (x-3)(x+3) we get:<BR>\n" );
document.write( "60(x+3) + 60(x-3) = 9(x-3)(x+3)<BR>\n" );
document.write( "60x + 180 + 60x - 180 = 9(x^2-9)<BR>\n" );
document.write( "120x = 9x^2 - 81<BR>\n" );
document.write( "0 = 9x^2 - 120X - 81<BR>\n" );
document.write( "0 = 3x^2 - 40X - 27<BR>\n" );
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document.write( "Since we can't factor, we must use the quadratic equation.  The solutions it gives is a positive and a negative answer.  Since it can't be negative we use the positive one.<BR>\n" );
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document.write( "x = 14 mph<BR>\n" );
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document.write( "Quadratic solution 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=3x%5E2%2B-40x%2B-27+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-40x%2B-27+=+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=%28-40%29%5E2-4%2A3%2A-27=1924 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-40%29%5E2-4%2A3%2A-27=1924\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1924 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--40%2B-sqrt%28+1924+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--40%2B-sqrt%28+1924+%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-%28-40%29%2Bsqrt%28+1924+%29%29%2F2%5C3+=+13.9772373998204 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-40%29%2Bsqrt%28+1924+%29%29%2F2%5C3+=+13.9772373998204\"   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-%28-40%29-sqrt%28+1924+%29%29%2F2%5C3+=+-0.643904066487103 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-40%29-sqrt%28+1924+%29%29%2F2%5C3+=+-0.643904066487103\"   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=3x%5E2%2B-40x%2B-27 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-40x%2B-27\"   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=3x%5E2%2B-40x%2B-27+=+3%28x-13.9772373998204%29%2A%28x--0.643904066487103%29 ALIGN=MIDDLE  ALT=\"3x%5E2%2B-40x%2B-27+=+3%28x-13.9772373998204%29%2A%28x--0.643904066487103%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 13.9772373998204, -0.643904066487103.\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+3%2Ax%5E2%2B-40%2Ax%2B-27+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-40%2Ax%2B-27+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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