document.write( "Question 189603: A jet flew from New york to los angeles, a distance of 4200km. the speed for the return trip was 100km/hr faster than the outbound speed. if the total trip took 13 hours, what was the speed from new york to los angeles. \n" ); document.write( "
Algebra.Com's Answer #142280 by nerdybill(7384)\"\" \"About 
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A jet flew from New york to los angeles, a distance of 4200km. the speed for the return trip was 100km/hr faster than the outbound speed. if the total trip took 13 hours, what was the speed from new york to los angeles.
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\n" ); document.write( "\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
\n" ); document.write( ".
\n" ); document.write( "In our case, you need to solve for 't':
\n" ); document.write( "t = d/r
\n" ); document.write( ".
\n" ); document.write( "Let x = outbound speed
\n" ); document.write( "then from \"the return trip was 100km/hr faster than the outbound speed.\"
\n" ); document.write( "x + 100 = inbound speed
\n" ); document.write( ".
\n" ); document.write( "4200/x + 4200/(x+100) = 13
\n" ); document.write( "Multiplying both sides by x(x+100) to get rid of our denominators:
\n" ); document.write( "4200(x+100) + 4200x = 13(x)(x+100)
\n" ); document.write( "4200x+ 420000 + 4200x = 13(x^2+100x)
\n" ); document.write( "8400x+ 420000 = 13x^2+1300x
\n" ); document.write( "420000 = 13x^2 - 7100x
\n" ); document.write( "0 = 13x^2 - 7100x - 420000
\n" ); document.write( "Applying the quadratic equation yields two solutions:
\n" ); document.write( "x = {600, -53.8462}
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\n" ); document.write( "You can toss out the negative solution leaving us with:
\n" ); document.write( "x = 600 km/hr outbound
\n" ); document.write( ".
\n" ); document.write( "Answer: 600 km/hr
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\n" ); document.write( "Details of quadratic to follow:
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"13x%5E2%2B-7100x%2B-420000+=+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=%28-7100%29%5E2-4%2A13%2A-420000=72250000\".
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\n" ); document.write( " Discriminant d=72250000 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--7100%2B-sqrt%28+72250000+%29%29%2F2%5Ca\".
\n" ); document.write( "
\n" ); document.write( " \"x%5B1%5D+=+%28-%28-7100%29%2Bsqrt%28+72250000+%29%29%2F2%5C13+=+600\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-7100%29-sqrt%28+72250000+%29%29%2F2%5C13+=+-53.8461538461538\"
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\n" ); document.write( " Quadratic expression \"13x%5E2%2B-7100x%2B-420000\" can be factored:
\n" ); document.write( " \"13x%5E2%2B-7100x%2B-420000+=+13%28x-600%29%2A%28x--53.8461538461538%29\"
\n" ); document.write( " Again, the answer is: 600, -53.8461538461538.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+13%2Ax%5E2%2B-7100%2Ax%2B-420000+%29\"

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