document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113995>Question 113995</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321319095/algebrahomeworkh>Introductory and Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The Hudson River flows at a rate of 3mph.  A patrol boat travels 60 miles upriver and returns in a total time of 9 hr.  What is the speed of the boat in still water?\r<BR>\n" );
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document.write( "D= rt upriver - 9r = 60 still water - 3rt = 60<BR>\n" );
document.write( "Have I set this equation up correctly?  Where do I go from here?  Please help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82960 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=82960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let r=speed of the boat in still water\r<BR>\n" );
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document.write( "When the boat goes upstream, we subtract 3mph from r to get (the boat is slowed by 3mph)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=%28r-3%29t%5B1%5D ALIGN=MIDDLE  ALT=\"60=%28r-3%29t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When the boat goes downstream, we can add 3mph to r to get (the boat is sped up by 3mph)\r<BR>\n" );
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document.write( "Now since the distance is the same we can set the two equations equal to one another to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F%28r-3%29=t%5B1%5D ALIGN=MIDDLE  ALT=\"60%2F%28r-3%29=t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D ALIGN=MIDDLE  ALT=\"t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F%28r%2B3%29=t%5B2%5D ALIGN=MIDDLE  ALT=\"60%2F%28r%2B3%29=t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D ALIGN=MIDDLE  ALT=\"t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the second equation\r<BR>\n" );
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document.write( "Since the total time was 9 hr, this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D%2Bt%5B2%5D=9 ALIGN=MIDDLE  ALT=\"t%5B1%5D%2Bt%5B2%5D=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F%28r-3%29%2B60%2F%28r%2B3%29=9 ALIGN=MIDDLE  ALT=\"60%2F%28r-3%29%2B60%2F%28r%2B3%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D=60%2F%28r-3%29 ALIGN=MIDDLE  ALT=\"t%5B1%5D=60%2F%28r-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D=60%2F%28r%2B3%29 ALIGN=MIDDLE  ALT=\"t%5B1%5D=60%2F%28r%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r-3%29%28r%2B3%29%2860%2F%28r-3%29%2B60%2F%28r%2B3%29%29=%28r-3%29%28r%2B3%29%289%29 ALIGN=MIDDLE  ALT=\"%28r-3%29%28r%2B3%29%2860%2F%28r-3%29%2B60%2F%28r%2B3%29%29=%28r-3%29%28r%2B3%29%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiply by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r-3%29%28r%2B3%29 ALIGN=MIDDLE  ALT=\"%28r-3%29%28r%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%28r%2B3%29%2B60%28r-3%29=%28r-3%29%28r%2B3%29%289%29 ALIGN=MIDDLE  ALT=\"60%28r%2B3%29%2B60%28r-3%29=%28r-3%29%28r%2B3%29%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%28r%2B3%29%2B60%28r-3%29=%28r%5E2-9%29%289%29 ALIGN=MIDDLE  ALT=\"60%28r%2B3%29%2B60%28r-3%29=%28r%5E2-9%29%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60r%2B180%2B60r-180=9r%5E2-81 ALIGN=MIDDLE  ALT=\"60r%2B180%2B60r-180=9r%5E2-81\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute again\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120r=9r%5E2-81 ALIGN=MIDDLE  ALT=\"120r=9r%5E2-81\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=9r%5E2-81-120r ALIGN=MIDDLE  ALT=\"0=9r%5E2-81-120r\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 120r from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=9r%5E2-120r-81 ALIGN=MIDDLE  ALT=\"0=9r%5E2-120r-81\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "Now let's use the quadratic formula to solve for r:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ar%5E2%2Bbr%2Bc=0 ALIGN=MIDDLE  ALT=\"ar%5E2%2Bbr%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Ar%5E2-120%2Ar-81=0 ALIGN=MIDDLE  ALT=\"9%2Ar%5E2-120%2Ar-81=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=9 ALIGN=MIDDLE  ALT=\"a=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-120 ALIGN=MIDDLE  ALT=\"b=-120\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-81 ALIGN=MIDDLE  ALT=\"c=-81\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28--120+%2B-+sqrt%28+%28-120%29%5E2-4%2A9%2A-81+%29%29%2F%282%2A9%29 ALIGN=MIDDLE  ALT=\"r+=+%28--120+%2B-+sqrt%28+%28-120%29%5E2-4%2A9%2A-81+%29%29%2F%282%2A9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=9, b=-120, and c=-81\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28120+%2B-+sqrt%28+%28-120%29%5E2-4%2A9%2A-81+%29%29%2F%282%2A9%29 ALIGN=MIDDLE  ALT=\"r+=+%28120+%2B-+sqrt%28+%28-120%29%5E2-4%2A9%2A-81+%29%29%2F%282%2A9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -120 to get 120\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28120+%2B-+sqrt%28+14400-4%2A9%2A-81+%29%29%2F%282%2A9%29 ALIGN=MIDDLE  ALT=\"r+=+%28120+%2B-+sqrt%28+14400-4%2A9%2A-81+%29%29%2F%282%2A9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -120 to get 14400  (note: remember when you square -120, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-120%29%5E2=-120%2A-120=14400 ALIGN=MIDDLE  ALT=\"%28-120%29%5E2=-120%2A-120=14400\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28120+%2B-+sqrt%28+14400%2B2916+%29%29%2F%282%2A9%29 ALIGN=MIDDLE  ALT=\"r+=+%28120+%2B-+sqrt%28+14400%2B2916+%29%29%2F%282%2A9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-81%2A9 ALIGN=MIDDLE  ALT=\"-4%2A-81%2A9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2916 ALIGN=MIDDLE  ALT=\"2916\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28120+%2B-+sqrt%28+17316+%29%29%2F%282%2A9%29 ALIGN=MIDDLE  ALT=\"r+=+%28120+%2B-+sqrt%28+17316+%29%29%2F%282%2A9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28120+%2B-+6%2Asqrt%28481%29%29%2F%282%2A9%29 ALIGN=MIDDLE  ALT=\"r+=+%28120+%2B-+6%2Asqrt%28481%29%29%2F%282%2A9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28120+%2B-+6%2Asqrt%28481%29%29%2F18 ALIGN=MIDDLE  ALT=\"r+=+%28120+%2B-+6%2Asqrt%28481%29%29%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 9 to get 18\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28120+%2B+6%2Asqrt%28481%29%29%2F18 ALIGN=MIDDLE  ALT=\"r+=+%28120+%2B+6%2Asqrt%28481%29%29%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28120+-+6%2Asqrt%28481%29%29%2F18 ALIGN=MIDDLE  ALT=\"r+=+%28120+-+6%2Asqrt%28481%29%29%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%2B120%2F18%2B6%2Asqrt%28481%29%2F18 ALIGN=MIDDLE  ALT=\"r=%2B120%2F18%2B6%2Asqrt%28481%29%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%2B120%2F18-6%2Asqrt%28481%29%2F18 ALIGN=MIDDLE  ALT=\"r=%2B120%2F18-6%2Asqrt%28481%29%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=20+%2F+3%2Bsqrt%28481%29%2F3 ALIGN=MIDDLE  ALT=\"r=20+%2F+3%2Bsqrt%28481%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=20+%2F+3-sqrt%28481%29%2F3 ALIGN=MIDDLE  ALT=\"r=20+%2F+3-sqrt%28481%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=13.9772373998204 ALIGN=MIDDLE  ALT=\"r=13.9772373998204\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-0.643904066487102 ALIGN=MIDDLE  ALT=\"r=-0.643904066487102\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "However, we cannot have a negative speed, so our only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=13.9772373998204 ALIGN=MIDDLE  ALT=\"r=13.9772373998204\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the speed of the boat in still water is about 13.977 mph </SPAN>\n" );
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