document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199535>Question 199535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hudson river flows at a rate of 5 miles per hour. a patrol boat travels 40miles upriver, and returns in a total time of 6 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 #149935 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=149935\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = speed of boat in still water<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the distance-rate-time formula<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40=%28x-3%29t ALIGN=MIDDLE  ALT=\"40=%28x-3%29t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=40 ALIGN=MIDDLE  ALT=\"d=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=x-5 ALIGN=MIDDLE  ALT=\"r=x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This equation represents the upstream journey.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28x-5%29=t ALIGN=MIDDLE  ALT=\"40%2F%28x-5%29=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5 ALIGN=MIDDLE  ALT=\"x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate \"t\";<BR>\n" );
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document.write( "So the expression for the time it takes to go upstream can be represented by the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28x-5%29 ALIGN=MIDDLE  ALT=\"40%2F%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-----------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the distance-rate-time formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40=%28x%2B5%29t ALIGN=MIDDLE  ALT=\"40=%28x%2B5%29t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=40 ALIGN=MIDDLE  ALT=\"d=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=x%2B5 ALIGN=MIDDLE  ALT=\"r=x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This equation represents the downstream journey<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28x%2B5%29=t ALIGN=MIDDLE  ALT=\"40%2F%28x%2B5%29=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5 ALIGN=MIDDLE  ALT=\"x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate \"t\";<BR>\n" );
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document.write( "So the expression for the time it takes to go downstream can be represented by the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"40%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now simply add the two time expressions to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28x-5%29%2B40%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"40%2F%28x-5%29%2B40%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28x-5%29%2B40%2F%28x%2B5%29=6 ALIGN=MIDDLE  ALT=\"40%2F%28x-5%29%2B40%2F%28x%2B5%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now set that expression equal to the total time of 6 hours<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%28x%2B5%29%2B40%28x-5%29=6%28x%2B5%29%28x-5%29 ALIGN=MIDDLE  ALT=\"40%28x%2B5%29%2B40%28x-5%29=6%28x%2B5%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <b>every</b> term by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear the denominators.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%28x%2B5%29%2B40%28x-5%29=6%28x%5E2-25%29 ALIGN=MIDDLE  ALT=\"40%28x%2B5%29%2B40%28x-5%29=6%28x%5E2-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40x%2B200%2B40x-200=6x%5E2-150 ALIGN=MIDDLE  ALT=\"40x%2B200%2B40x-200=6x%5E2-150\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40x%2B200%2B40x-200-6x%5E2%2B150=0 ALIGN=MIDDLE  ALT=\"40x%2B200%2B40x-200-6x%5E2%2B150=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2 ALIGN=MIDDLE  ALT=\"6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides. Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150 ALIGN=MIDDLE  ALT=\"150\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%5E2%2B80x%2B150=0 ALIGN=MIDDLE  ALT=\"-6x%5E2%2B80x%2B150=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Notice we have a quadratic in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2%2BBx%2BC ALIGN=MIDDLE  ALT=\"Ax%5E2%2BBx%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-6 ALIGN=MIDDLE  ALT=\"A=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=80 ALIGN=MIDDLE  ALT=\"B=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=150 ALIGN=MIDDLE  ALT=\"C=150\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for \"x\":\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%2880%29+%2B-+sqrt%28+%2880%29%5E2-4%28-6%29%28150%29+%29%29%2F%282%28-6%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%2880%29+%2B-+sqrt%28+%2880%29%5E2-4%28-6%29%28150%29+%29%29%2F%282%28-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-6 ALIGN=MIDDLE  ALT=\"A=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=80 ALIGN=MIDDLE  ALT=\"B=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=150 ALIGN=MIDDLE  ALT=\"C=150\"   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=x+=+%28-80+%2B-+sqrt%28+6400-4%28-6%29%28150%29+%29%29%2F%282%28-6%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-80+%2B-+sqrt%28+6400-4%28-6%29%28150%29+%29%29%2F%282%28-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80 ALIGN=MIDDLE  ALT=\"80\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6400 ALIGN=MIDDLE  ALT=\"6400\"   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=x+=+%28-80+%2B-+sqrt%28+6400%2B3600+%29%29%2F%282%28-6%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-80+%2B-+sqrt%28+6400%2B3600+%29%29%2F%282%28-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286400--3600%29 ALIGN=MIDDLE  ALT=\"sqrt%286400--3600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286400%2B3600%29 ALIGN=MIDDLE  ALT=\"sqrt%286400%2B3600%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=x+=+%28-80+%2B-+sqrt%28+10000+%29%29%2F%282%28-6%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-80+%2B-+sqrt%28+10000+%29%29%2F%282%28-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6400 ALIGN=MIDDLE  ALT=\"6400\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3600 ALIGN=MIDDLE  ALT=\"3600\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000 ALIGN=MIDDLE  ALT=\"10000\"   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=x+=+%28-80+%2B-+sqrt%28+10000+%29%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-80+%2B-+sqrt%28+10000+%29%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   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=x+=+%28-80+%2B-+100%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-80+%2B-+100%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000 ALIGN=MIDDLE  ALT=\"10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   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=x+=+%28-80+%2B+100%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-80+%2B+100%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-80+-+100%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-80+-+100%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2820%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=+%2820%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-180%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=++%28-180%29%2F%28-12%29\"   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=x+=+-5%2F3 ALIGN=MIDDLE  ALT=\"x+=+-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the <i>possible</i> solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-5%2F3 ALIGN=MIDDLE  ALT=\"x+=+-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "However, you can't have a negative speed. So the only answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the speed of the boat in still water is 15 mph. </SPAN>\n" );
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