document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171089>Question 171089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the current in a stream moves at a speed of 10 mph. A boat travels 29 miles upstreamand 29 miles downstream in a total time of 8 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 #126313 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126313\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first thing I would do would be to make complaint about being given this computational horror, but here goes anyway.\r<BR>\n" );
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document.write( "Assume <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the rate of the boat in still water.  The upstream rate is the speed of the boat in still water minus the current speed:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-10 ALIGN=MIDDLE  ALT=\"r-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The downstream rate is the rate in still water PLUS the current speed:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2B10 ALIGN=MIDDLE  ALT=\"r%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Assume <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the time it takes to go upstream 29 miles, then since the total time of the trip is 8 hours, the time to go downstream must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-t ALIGN=MIDDLE  ALT=\"8-t\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Using the basic relationship <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;\" >, written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=d%2Fr ALIGN=MIDDLE  ALT=\"t=d%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the upstream trip can be expressed as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=29%2F%28r-10%29 ALIGN=MIDDLE  ALT=\"t=29%2F%28r-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Likewise, the downstream trip can be expressed as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-t=29%2F%28r%2B10%29 ALIGN=MIDDLE  ALT=\"8-t=29%2F%28r%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Isolating <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > in both equations produces:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=29%2F%28r%2B10%29 ALIGN=MIDDLE  ALT=\"t=29%2F%28r%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-29%29%2F%28r-10%29%2B8 ALIGN=MIDDLE  ALT=\"t=%28-29%29%2F%28r-10%29%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This gives us two different expressions for the elapsed time of the upstream trip in terms of the rate of the boat in still water.  We can set these two expressions equal to each other:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29%2F%28r%2B10%29=%28-29%29%2F%28r-10%29%2B8 ALIGN=MIDDLE  ALT=\"29%2F%28r%2B10%29=%28-29%29%2F%28r-10%29%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Application of the common denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2-100 ALIGN=MIDDLE  ALT=\"r%5E2-100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, setting the resulting numerators equal to each other and collecting like terms results in the following: (Intermediate steps left as an exercise for the student)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r%5E2-29r%2B400=0 ALIGN=MIDDLE  ALT=\"4r%5E2-29r%2B400=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Applying 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-%28-29%29+%2B-+sqrt%28+%28-29%29%5E2-4%2A%284%29%2A%28-400%29+%29%29%2F%282%2A4%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-29%29+%2B-+sqrt%28+%28-29%29%5E2-4%2A%284%29%2A%28-400%29+%29%29%2F%282%2A4%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%5B1%5D+=+%2829+%2B+sqrt%287241%29%29%2F8 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%2829+%2B+sqrt%287241%29%29%2F8\"   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%5B2%5D+=+%2829+-+sqrt%287241%29%29%2F8 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%2829+-+sqrt%287241%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this root less than zero, so exclude as extraneous}\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2829+%2B+sqrt%287241%29%29%2F8 ALIGN=MIDDLE  ALT=\"%2829+%2B+sqrt%287241%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be simplified further because 7241 has no perfect square factors and therefore is the exact answer.  A little calculator work results in a numerical approximation of 14.26 hours elapsed time for the upstream trip.  This answer should properly be rounded to the nearest whole hour because your input values of distance, time, and current speed were all expressed in whole numbers and it is  incorrect (unless greater precision is specified in the problem statement) to express a result of a computation involving measurements to a greater precision than the least precise input measurement.\r<BR>\n" );
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document.write( "Calculating the upstream rate, downstream rate, and time for each part of the trip to verify the sum is approximately equal to 8 hours, thereby verifying the answer, is left as an exercise for the student.  Enjoy. </SPAN>\n" );
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