document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167652>Question 167652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a motorboat heads upstream for a distance of 24 miles on the Illinois River, whose current is running at 3mph. the trip up and back takes a total of 6 hours. assuming that the boat maintained a constant speed relative to the water, what is this constant speed? -- i've never been great at calculus word problems, thank u for all the help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123552 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=123552\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Downstream:\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;\" > Start with 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=24=rt ALIGN=MIDDLE  ALT=\"24=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in d=24\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=%28r%2B3%29t ALIGN=MIDDLE  ALT=\"24=%28r%2B3%29t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2B3 ALIGN=MIDDLE  ALT=\"r%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since the speed of the river sped up the boat 3 mph)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=24%2F%28r%2B3%29 ALIGN=MIDDLE  ALT=\"t=24%2F%28r%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2B3 ALIGN=MIDDLE  ALT=\"r%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and rearrange to isolate \"t\"\r<BR>\n" );
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document.write( "So the time it took to go downstream was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=24%2F%28r%2B3%29 ALIGN=MIDDLE  ALT=\"t=24%2F%28r%2B3%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( "Upstream:\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;\" > Start with 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=24=rt ALIGN=MIDDLE  ALT=\"24=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in d=24\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=%28r-3%29t ALIGN=MIDDLE  ALT=\"24=%28r-3%29t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-3 ALIGN=MIDDLE  ALT=\"r-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since the speed of the river slowed the boat 3 mph)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=24%2F%28r-3%29 ALIGN=MIDDLE  ALT=\"t=24%2F%28r-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-3 ALIGN=MIDDLE  ALT=\"r-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and rearrange to isolate \"t\"\r<BR>\n" );
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document.write( "So the time it took to go upstream was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=24%2F%28r-3%29 ALIGN=MIDDLE  ALT=\"t=24%2F%28r-3%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( "Now simply add the two times and set them equal to the total time (6 hours) to get\r<BR>\n" );
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document.write( "Downstream Time + Upstream Time = Total Time\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=24%2F%28r%2B3%29%2B24%2F%28r-3%29=6 ALIGN=MIDDLE  ALT=\"24%2F%28r%2B3%29%2B24%2F%28r-3%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2824%2Fcross%28%28r%2B3%29%29%29cross%28%28r%2B3%29%29%28r-3%29%2B%2824%2Fcross%28%28r-3%29%29%29%28r%2B3%29cross%28%28r-3%29%29=6%28r%2B3%29%28r-3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2B3%29%28r-3%29 ALIGN=MIDDLE  ALT=\"%28r%2B3%29%28r-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%28r-3%29%2B24%28r%2B3%29=6%28r%2B3%29%28r-3%29 ALIGN=MIDDLE  ALT=\"24%28r-3%29%2B24%28r%2B3%29=6%28r%2B3%29%28r-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%28r-3%29%2B24%28r%2B3%29=6%28r%5E2-9%29 ALIGN=MIDDLE  ALT=\"24%28r-3%29%2B24%28r%2B3%29=6%28r%5E2-9%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=24r-72%2B24r%2B72=6r%5E2-54 ALIGN=MIDDLE  ALT=\"24r-72%2B24r%2B72=6r%5E2-54\"   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=48r=6r%5E2-54 ALIGN=MIDDLE  ALT=\"48r=6r%5E2-54\"   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=6r%5E2-54-48r ALIGN=MIDDLE  ALT=\"0=6r%5E2-54-48r\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 48r 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=6r%5E2-48r-54 ALIGN=MIDDLE  ALT=\"0=6r%5E2-48r-54\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the 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=ar%5E2%2Bbr%2Bc ALIGN=MIDDLE  ALT=\"ar%5E2%2Bbr%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=-48 ALIGN=MIDDLE  ALT=\"b=-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-54 ALIGN=MIDDLE  ALT=\"c=-54\"   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 r\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%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"r+=+%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=r+=+%28-%28-48%29+%2B-+sqrt%28+%28-48%29%5E2-4%286%29%28-54%29+%29%29%2F%282%286%29%29 ALIGN=MIDDLE  ALT=\"r+=+%28-%28-48%29+%2B-+sqrt%28+%28-48%29%5E2-4%286%29%28-54%29+%29%29%2F%282%286%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=-48 ALIGN=MIDDLE  ALT=\"b=-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-54 ALIGN=MIDDLE  ALT=\"c=-54\"   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+=+%2848+%2B-+sqrt%28+%28-48%29%5E2-4%286%29%28-54%29+%29%29%2F%282%286%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2848+%2B-+sqrt%28+%28-48%29%5E2-4%286%29%28-54%29+%29%29%2F%282%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48 ALIGN=MIDDLE  ALT=\"-48\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   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+=+%2848+%2B-+sqrt%28+2304-4%286%29%28-54%29+%29%29%2F%282%286%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2848+%2B-+sqrt%28+2304-4%286%29%28-54%29+%29%29%2F%282%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48 ALIGN=MIDDLE  ALT=\"-48\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304 ALIGN=MIDDLE  ALT=\"2304\"   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+=+%2848+%2B-+sqrt%28+2304--1296+%29%29%2F%282%286%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2848+%2B-+sqrt%28+2304--1296+%29%29%2F%282%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%286%29%28-54%29 ALIGN=MIDDLE  ALT=\"4%286%29%28-54%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1296 ALIGN=MIDDLE  ALT=\"-1296\"   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+=+%2848+%2B-+sqrt%28+2304%2B1296+%29%29%2F%282%286%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2848+%2B-+sqrt%28+2304%2B1296+%29%29%2F%282%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282304--1296%29 ALIGN=MIDDLE  ALT=\"sqrt%282304--1296%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282304%2B1296%29 ALIGN=MIDDLE  ALT=\"sqrt%282304%2B1296%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=r+=+%2848+%2B-+sqrt%28+3600+%29%29%2F%282%286%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2848+%2B-+sqrt%28+3600+%29%29%2F%282%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304 ALIGN=MIDDLE  ALT=\"2304\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1296 ALIGN=MIDDLE  ALT=\"1296\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3600 ALIGN=MIDDLE  ALT=\"3600\"   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+=+%2848+%2B-+sqrt%28+3600+%29%29%2F%2812%29 ALIGN=MIDDLE  ALT=\"r+=+%2848+%2B-+sqrt%28+3600+%29%29%2F%2812%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=r+=+%2848+%2B-+60%29%2F%2812%29 ALIGN=MIDDLE  ALT=\"r+=+%2848+%2B-+60%29%2F%2812%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=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=60 ALIGN=MIDDLE  ALT=\"60\"   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+=+%2848+%2B+60%29%2F%2812%29 ALIGN=MIDDLE  ALT=\"r+=+%2848+%2B+60%29%2F%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2848+-+60%29%2F%2812%29 ALIGN=MIDDLE  ALT=\"r+=+%2848+-+60%29%2F%2812%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=r+=+%28108%29%2F%2812%29 ALIGN=MIDDLE  ALT=\"r+=+%28108%29%2F%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=++%28-12%29%2F%2812%29 ALIGN=MIDDLE  ALT=\"r+=++%28-12%29%2F%2812%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=r+=+9 ALIGN=MIDDLE  ALT=\"r+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-1 ALIGN=MIDDLE  ALT=\"r+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the possible answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+9 ALIGN=MIDDLE  ALT=\"r+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-1 ALIGN=MIDDLE  ALT=\"r+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "However, a negative speed doesn't make much sense. So the only answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+9 ALIGN=MIDDLE  ALT=\"r+=+9\"   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 solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+9 ALIGN=MIDDLE  ALT=\"r+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the boat was going 9 mph relative to the water. \r<BR>\n" );
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document.write( "In other words, the speed of the boat in still water is 9 mph. </SPAN>\n" );
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