document.write( "Question 1050063: A 3 mile boat race takes place in Detroit every year. The current in the river is 4 mph. What is the speed od the boat in still water if the total time of upstream and downstream is 1 hour \n" ); document.write( "
Algebra.Com's Answer #665676 by josgarithmetic(39620)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "                  SPEED            TIME           DISTANCE\r\n" );
document.write( "UPSTREAM          r-4\r\n" );
document.write( "DOWNSTREAM        r+4\r\n" );
document.write( "TOTAL                               1              3\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you assign time up and time down each their own variable, then you would have THREE variables but still only TWO equations for the \"totals\". The two totals, one of time and one of distance, allows just picking one of these totals for assigning just one variable to either up or down stream.\r
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document.write( "                  SPEED            TIME           DISTANCE\r\n" );
document.write( "UPSTREAM          r-4               t\r\n" );
document.write( "DOWNSTREAM        r+4              1-t\r\n" );
document.write( "TOTAL                               1              3\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now, fill-in the distance expressions.
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document.write( "                  SPEED            TIME           DISTANCE\r\n" );
document.write( "UPSTREAM          r-4               t             (r-4)*t\r\n" );
document.write( "DOWNSTREAM        r+4              1-t           (r+4)(1-t)\r\n" );
document.write( "TOTAL                               1              3\r\n" );
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\n" ); document.write( "Still not adequate.\r
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\n" ); document.write( "\n" ); document.write( "Check the description carefully! \"3 mile boat race\", and \"upstream and downstream\". Maybe the round trip was 3 miles, and then up and downstreams are each one-and-a-half miles.\r
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\n" ); document.write( "\n" ); document.write( "Let's try that understanding, and use variables assigned a little differently:
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document.write( "                  SPEED            TIME           DISTANCE\r\n" );
document.write( "UPSTREAM          r-4               x              1.5\r\n" );
document.write( "DOWNSTREAM        r+4               y              1.5\r\n" );
document.write( "TOTAL                               1              3\r\n" );
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\n" ); document.write( "Resulting system of equations: \"system%28%28r-4%29x=1.5%2C%28r%2B4%29y=1.5%2Cx%2By=1%29\"
\n" ); document.write( "Three equations in three unknown variables. Not linear system; but various ways possible to solve the system.\r
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\n" ); document.write( "\n" ); document.write( "POSSIBLE STEPS
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\n" ); document.write( "\"r-4=1.5%2Fx\"
\n" ); document.write( "\"r=4%2B1.5%2Fx\"
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\n" ); document.write( "\"r%2B4=1.5%2Fy\"
\n" ); document.write( "\"r=1.5%2Fy-4\"
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\n" ); document.write( "\"1.5%2Fx%2B4=1.5%2Fy-4\"
\n" ); document.write( "\"aFewFurtherSteps\"
\n" ); document.write( "\"8xy=1.5x-1.5y\"
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\n" ); document.write( "REVISED SYSTEM OF EQUATIONS: \"system%288xy=1.5x-1.5y%2Cx%2By=1%29\"
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\n" ); document.write( "using y=1-x and substituting,
\n" ); document.write( "\"8x%281-x%29=1.5x-1.5%281-x%29\"
\n" ); document.write( "\"andThenAFewSteps\"
\n" ); document.write( "\"highlight_green%2816x%5E2-16x-3=0%29\"
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\n" ); document.write( "\"x=%284%2B-sqrt%2813%29%29%2F8\"
\n" ); document.write( "Unfinished here...\r
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\n" ); document.write( "\n" ); document.write( "STEPS(DESCRIPTIVE)-ANOTHER APPROACH
\n" ); document.write( "Another approach can use y=1-x and substitute this into each of the equations containing r. Doing so and carrying through the algebra will give \"system%28rx%2B4x-r=2.5%2Crx-4x=1.5%29%29\"
\n" ); document.write( "from which you can obtain
\n" ); document.write( "\"highlight_green%28r%281.5%2F%28r-4%29%29%2B4%281.5%2F%28r-4%29%29-r=2.5%29\"
\n" ); document.write( "again, skipping some of the next steps here, but...
\n" ); document.write( "\"highlight%28r%5E2-3r-16=0%29\"
\n" ); document.write( "and you can continue some algebraic steps with general solution formula for quadratic equation to solve for r, which is what the question asked for.
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\n" ); document.write( "If all this work is reliable, then \"highlight%28r=%283%2B-+sqrt%2873%29%29%2F2%29\" but you need to use the PLUS form! \n" ); document.write( "
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