document.write( "Question 298137: a plane traveling 450 miles per hour can go 1000 miles with the wind in 1/2 hour less than when traveling against the wind. Find the speed of the wind. \n" ); document.write( "
Algebra.Com's Answer #214618 by ankor@dixie-net.com(22740)\"\" \"About 
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a plane traveling 450 miles per hour can go 1000 miles with the wind in 1/2 hour
\n" ); document.write( " less than when traveling against the wind.
\n" ); document.write( "Find the speed of the wind.
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\n" ); document.write( "Let w = speed of the wind
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\n" ); document.write( "Plane effective ground speed:
\n" ); document.write( "(450+w) = with the wind
\n" ); document.write( "(450-w) = against the wind
\n" ); document.write( ":
\n" ); document.write( "Write a time equation, time = dist/speed:
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\n" ); document.write( "Time against - time with = .5 hr
\n" ); document.write( "\"1000%2F%28%28450-w%29%29\" - \"100%2F%28%28450%2Bw%29%29\" = .5
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\n" ); document.write( "Multiply by (450+w)(45-w), resulting in
\n" ); document.write( "1000(450+w) - 1000(450-w) = .5
\n" ); document.write( ":
\n" ); document.write( "450000 + 1000w - 450000+ 1000w = .5(450-w)(450+w)
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\n" ); document.write( "2000w = .5(202500 - w^2)
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\n" ); document.write( "2000w = 101250 - .5w^2
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\n" ); document.write( "Arrange as a quadratic equation on the left
\n" ); document.write( ".5w^2 + 2000w - 101250 = 0
\n" ); document.write( "multiply by 1
\n" ); document.write( "w^2 + 4000w - 202500 = 0
\n" ); document.write( "Factor this to
\n" ); document.write( "(w+4050)(w-50) = 0
\n" ); document.write( "positive solution
\n" ); document.write( "w = 50 mph is the wind
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\n" ); document.write( "Check solution by finding the times
\n" ); document.write( "1000/400 = 2.5
\n" ); document.write( "1000/500 = 2.0
\n" ); document.write( "--------------
\n" ); document.write( "differs by: .5 hr \n" ); document.write( "
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