document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155379>Question 155379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4.	The Hudson River flows at a rate of 3 miles 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 #114416 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=114416\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 4\r<BR>\n" );
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document.write( "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=60=%28x-3%29t ALIGN=MIDDLE  ALT=\"60=%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=60 ALIGN=MIDDLE  ALT=\"d=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=x-3 ALIGN=MIDDLE  ALT=\"r=x-3\"   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=60%2F%28x-3%29=t ALIGN=MIDDLE  ALT=\"60%2F%28x-3%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-3 ALIGN=MIDDLE  ALT=\"x-3\"   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=60%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"60%2F%28x-3%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=60=%28x%2B3%29t ALIGN=MIDDLE  ALT=\"60=%28x%2B3%29t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=60 ALIGN=MIDDLE  ALT=\"d=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=x%2B3 ALIGN=MIDDLE  ALT=\"r=x%2B3\"   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=60%2F%28x%2B3%29=t ALIGN=MIDDLE  ALT=\"60%2F%28x%2B3%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%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   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=60%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"60%2F%28x%2B3%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=60%2F%28x-3%29%2B60%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"60%2F%28x-3%29%2B60%2F%28x%2B3%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=60%2F%28x-3%29%2B60%2F%28x%2B3%29=9 ALIGN=MIDDLE  ALT=\"60%2F%28x-3%29%2B60%2F%28x%2B3%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now set that expression equal to the total time of 9 hours<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%28x%2B3%29%2B60%28x-3%29=9%28x%2B3%29%28x-3%29 ALIGN=MIDDLE  ALT=\"60%28x%2B3%29%2B60%28x-3%29=9%28x%2B3%29%28x-3%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%2B3%29%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x-3%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=60x%2B180%2B60x-180=9x%5E2-81 ALIGN=MIDDLE  ALT=\"60x%2B180%2B60x-180=9x%5E2-81\"   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=-9x%5E2%2B120x%2B81=0 ALIGN=MIDDLE  ALT=\"-9x%5E2%2B120x%2B81=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 equation 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=-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( "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-%28120%29+%2B-+sqrt%28+%28120%29%5E2-4%28-9%29%2881%29+%29%29%2F%282%28-9%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28120%29+%2B-+sqrt%28+%28120%29%5E2-4%28-9%29%2881%29+%29%29%2F%282%28-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <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=x+=+%28-120+%2B-+sqrt%28+14400-4%28-9%29%2881%29+%29%29%2F%282%28-9%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+sqrt%28+14400-4%28-9%29%2881%29+%29%29%2F%282%28-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120 ALIGN=MIDDLE  ALT=\"120\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14400 ALIGN=MIDDLE  ALT=\"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=x+=+%28-120+%2B-+sqrt%28+14400--2916+%29%29%2F%282%28-9%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+sqrt%28+14400--2916+%29%29%2F%282%28-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-9%29%2881%29 ALIGN=MIDDLE  ALT=\"4%28-9%29%2881%29\"   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=x+=+%28-120+%2B-+sqrt%28+14400%2B2916+%29%29%2F%282%28-9%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+sqrt%28+14400%2B2916+%29%29%2F%282%28-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2814400--2916%29 ALIGN=MIDDLE  ALT=\"sqrt%2814400--2916%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2814400%2B2916%29 ALIGN=MIDDLE  ALT=\"sqrt%2814400%2B2916%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+=+%28-120+%2B-+sqrt%28+17316+%29%29%2F%282%28-9%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+sqrt%28+17316+%29%29%2F%282%28-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14400 ALIGN=MIDDLE  ALT=\"14400\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2916 ALIGN=MIDDLE  ALT=\"2916\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17316 ALIGN=MIDDLE  ALT=\"17316\"   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+=+%28-120+%2B-+sqrt%28+17316+%29%29%2F%28-18%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+sqrt%28+17316+%29%29%2F%28-18%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=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18 ALIGN=MIDDLE  ALT=\"-18\"   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+=+%28-120+%2B-+6%2Asqrt%28481%29%29%2F%28-18%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+6%2Asqrt%28481%29%29%2F%28-18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, 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( "So the answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-120%2B6%2Asqrt%28481%29%29%2F%28-18%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120%2B6%2Asqrt%28481%29%29%2F%28-18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-120-6%2Asqrt%28481%29%29%2F%28-18%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120-6%2Asqrt%28481%29%29%2F%28-18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "which approximate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.644 ALIGN=MIDDLE  ALT=\"x=-0.644\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13.977 ALIGN=MIDDLE  ALT=\"x=13.977\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Since a negative speed doesn't make sense in this problem, this means that the only solution is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13.977 ALIGN=MIDDLE  ALT=\"x=13.977\"   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 approximately 13.98 mph (rounded to the nearest hundredth).<BR>\n" );
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