document.write( "Question 172939This question is from textbook Introductory Algebra
\n" ); document.write( ": The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water? \n" ); document.write( "
Algebra.Com's Answer #127811 by nerdybill(7384)\"\" \"About 
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The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water?
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\n" ); document.write( "You will need to apply the \"distance\" formula:
\n" ); document.write( "d = rt
\n" ); document.write( "where
\n" ); document.write( "d is distance
\n" ); document.write( "r is rate or speed
\n" ); document.write( "t is time
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\n" ); document.write( "Solving for t:
\n" ); document.write( "d = rt
\n" ); document.write( "d/r = t
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\n" ); document.write( "Let x = speed of boat in still water
\n" ); document.write( "45/(x+3) + 45/(x-3) = 8
\n" ); document.write( "Multiplying both sides by:(x+3)(x-3)
\n" ); document.write( "45(x-3) + 45(x+3) = 8(x+3)(x-3)
\n" ); document.write( "45[(x-3) + (x+3)] = 8(x^2-9)
\n" ); document.write( "45[2x] = 8x^2-72
\n" ); document.write( "90x = 8x^2-72
\n" ); document.write( "0 = 8x^2-90x-72
\n" ); document.write( "0 = 4x^2-45x-36
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\n" ); document.write( "Since we can't factor, we solve with the quadratic equation. Doing so will yield:
\n" ); document.write( "x = {12, -0.75}
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\n" ); document.write( "We can ignore the negative solution leaving us with
\n" ); document.write( "x = 12 mph (speed of boat in still waters)
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\n" ); document.write( "Details of quadratic follows:
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"4x%5E2%2B-45x%2B-36+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-45%29%5E2-4%2A4%2A-36=2601\".
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\n" ); document.write( " Discriminant d=2601 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--45%2B-sqrt%28+2601+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-45%29%2Bsqrt%28+2601+%29%29%2F2%5C4+=+12\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-45%29-sqrt%28+2601+%29%29%2F2%5C4+=+-0.75\"
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\n" ); document.write( " Quadratic expression \"4x%5E2%2B-45x%2B-36\" can be factored:
\n" ); document.write( " \"4x%5E2%2B-45x%2B-36+=+4%28x-12%29%2A%28x--0.75%29\"
\n" ); document.write( " Again, the answer is: 12, -0.75.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-45%2Ax%2B-36+%29\"
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