document.write( "Question 152709: The speed of an airplane in still air is 250 km. The plane travels 632 km
\n" ); document.write( "against the wind and 1343 km with the wind in a total time of 15 hours. What is the speed of the wind? \r
\n" ); document.write( "\n" ); document.write( "Thank You. I have been at this problem for hours. \n" ); document.write( "
Algebra.Com's Answer #112266 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
The speed of an airplane in still air is 250 km. The plane travels 632 km
\n" ); document.write( "against the wind and 1343 km with the wind in a total time of 15 hours. What is the speed of the wind?
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\n" ); document.write( "Write down what you know:
\n" ); document.write( "Let x = speed of the wind
\n" ); document.write( "then
\n" ); document.write( "(250+x) = the speed of the plane with the wind
\n" ); document.write( "and
\n" ); document.write( "(250-x) = the speed against the wind
\n" ); document.write( ":
\n" ); document.write( "Write a time equation: Time = Dist/speed
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\n" ); document.write( "Time with + time against = 15 hrs
\n" ); document.write( "\"1343%2F%28%28250%2Bx%29%29\" + \"632%2F%28%28250-x%29%29\" = 15
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\n" ); document.write( "Multiply equation by the common denominator: (250+x)(250-x), results
\n" ); document.write( "1343(250-x) + 632(250+x) = 15(250+x)(250-x)
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\n" ); document.write( "335750 - 1343x + 158000 + 632x = 15(62500 - x^2); FOILed
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\n" ); document.write( "493750 - 711x = 937500 - 15x^2
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "15x^2 - 711x + 493750 - 937500 = 0
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\n" ); document.write( "15x^2 - 711x - 443750 = 0
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\n" ); document.write( "A nasty equation to be solved by the quadratic formula
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "In this problem a=15; b=-711; c= -443750
\n" ); document.write( "\"x+=+%28-%28-711%29+%2B-+sqrt%28-711%5E2+-+4+%2A+15+%2A-443750+%29%29%2F%282%2A15%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%28711+%2B-+sqrt%28505521+%2B+26625000+%29%29%2F%2830%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%28711+%2B-+sqrt%2827130521+%29%29%2F%2830%29+\"
\n" ); document.write( "The positive solution
\n" ); document.write( "\"x+=+%28711+%2B+5208.7%29%2F%2830%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+5919.7%2F30+\"
\n" ); document.write( "x = 197.3 is the speed of the wind
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\n" ); document.write( "Check this rather extreme solution by finding the total time:
\n" ); document.write( "Speed with = 447.3; against = 52.7
\n" ); document.write( "Using a calc
\n" ); document.write( "1343/447.3 + 632/52.7 =
\n" ); document.write( "3.00 + 11.99 = 14.99 ~ 15 hrs\r
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