document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173348>Question 173348</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321269470/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have a word problem but I am stuck.\r<BR>\n" );
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document.write( "the current in a stream moves at a speed of 3mph.  A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hours.  What is the speed of the boat in still water?\r<BR>\n" );
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document.write( "45/r-3 + 45/r+3 = 8<BR>\n" );
document.write( "45(r+3) + 45(r-3)= 8(r+3)(r-3)<BR>\n" );
document.write( "90r = 8r^2 - 72<BR>\n" );
document.write( "and I'm stuck </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128194 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=128194\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You're off to a great start. I'll start where you left off.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90r+=+8r%5E2+-+72 ALIGN=MIDDLE  ALT=\"90r+=+8r%5E2+-+72\"   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=0+=+8r%5E2+-+72-90r ALIGN=MIDDLE  ALT=\"0+=+8r%5E2+-+72-90r\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 90r 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=+8r%5E2-90r+-+72 ALIGN=MIDDLE  ALT=\"+0=+8r%5E2-90r+-+72\"   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=8 ALIGN=MIDDLE  ALT=\"a=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-90 ALIGN=MIDDLE  ALT=\"b=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-72 ALIGN=MIDDLE  ALT=\"c=-72\"   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-%28-90%29+%2B-+sqrt%28+%28-90%29%5E2-4%288%29%28-72%29+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"r+=+%28-%28-90%29+%2B-+sqrt%28+%28-90%29%5E2-4%288%29%28-72%29+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8 ALIGN=MIDDLE  ALT=\"a=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-90 ALIGN=MIDDLE  ALT=\"b=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-72 ALIGN=MIDDLE  ALT=\"c=-72\"   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+=+%2890+%2B-+sqrt%28+%28-90%29%5E2-4%288%29%28-72%29+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2890+%2B-+sqrt%28+%28-90%29%5E2-4%288%29%28-72%29+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-90 ALIGN=MIDDLE  ALT=\"-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90 ALIGN=MIDDLE  ALT=\"90\"   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+=+%2890+%2B-+sqrt%28+8100-4%288%29%28-72%29+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2890+%2B-+sqrt%28+8100-4%288%29%28-72%29+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-90 ALIGN=MIDDLE  ALT=\"-90\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8100 ALIGN=MIDDLE  ALT=\"8100\"   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+=+%2890+%2B-+sqrt%28+8100--2304+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2890+%2B-+sqrt%28+8100--2304+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%288%29%28-72%29 ALIGN=MIDDLE  ALT=\"4%288%29%28-72%29\"   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+=+%2890+%2B-+sqrt%28+8100%2B2304+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2890+%2B-+sqrt%28+8100%2B2304+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288100--2304%29 ALIGN=MIDDLE  ALT=\"sqrt%288100--2304%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288100%2B2304%29 ALIGN=MIDDLE  ALT=\"sqrt%288100%2B2304%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+=+%2890+%2B-+sqrt%28+10404+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"r+=+%2890+%2B-+sqrt%28+10404+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8100 ALIGN=MIDDLE  ALT=\"8100\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <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 get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10404 ALIGN=MIDDLE  ALT=\"10404\"   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+=+%2890+%2B-+sqrt%28+10404+%29%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"r+=+%2890+%2B-+sqrt%28+10404+%29%29%2F%2816%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=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   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+=+%2890+%2B-+102%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"r+=+%2890+%2B-+102%29%2F%2816%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=10404 ALIGN=MIDDLE  ALT=\"10404\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=102 ALIGN=MIDDLE  ALT=\"102\"   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+=+%2890+%2B+102%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"r+=+%2890+%2B+102%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%2890+-+102%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"r+=+%2890+-+102%29%2F%2816%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+=+%28192%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"r+=+%28192%29%2F%2816%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%2816%29 ALIGN=MIDDLE  ALT=\"r+=++%28-12%29%2F%2816%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+=+12 ALIGN=MIDDLE  ALT=\"r+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-3%2F4 ALIGN=MIDDLE  ALT=\"r+=+-3%2F4\"   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+=+12 ALIGN=MIDDLE  ALT=\"r+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-3%2F4 ALIGN=MIDDLE  ALT=\"r+=+-3%2F4\"   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( "However, a negative speed doesn't make sense. So we'll discard the possible solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+-3%2F4 ALIGN=MIDDLE  ALT=\"r+=+-3%2F4\"   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+=+12 ALIGN=MIDDLE  ALT=\"r+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the speed of the boat in still water is 12 mph.<BR>\n" );
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