document.write( "Question 53603: 1. A plane flies 720 miles against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10h, what is the plane's speed in still air?\r
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Algebra.Com's Answer #35828 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
1. A plane flies 720 miles against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10h, what is the plane's speed in still air?
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\n" ); document.write( "Let the planes speed in still air = s
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\n" ); document.write( "Speed with the wind: (s+30)
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\n" ); document.write( "Speed against the wind: (s-30)
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\n" ); document.write( "Distance out and back is the same; 720 mi
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\n" ); document.write( "Write a time equation: Time = dist/speed
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\n" ); document.write( "Time out + time back = 10 hrs
\n" ); document.write( " \"720%2F%28s-30%29\" + \"720%2F%28s%2B30%29\" = 10
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\n" ); document.write( "To get rid of the denominators, mult eq by (s-30)(s+30), resulting in:
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\n" ); document.write( "720(s+30) + 720(s-30) = 10(s-30)(s+30)
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\n" ); document.write( "720s + 21600 + 720s - 21600 = 10(s^2 - 900)
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\n" ); document.write( "1440s = 10s^2 - 9000
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\n" ); document.write( "0 = 10s^2 -1440s - 9000 a quadratic equation
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\n" ); document.write( "s^2 - 144s - 900 = 0 Simplified, divided equation by 10
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\n" ); document.write( "Factors to: (s + 6) (s - 150) = 0
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\n" ); document.write( "Obvious solution: s = +150 mph
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\n" ); document.write( "Check:
\n" ); document.write( "720/120 + 720/180 =
\n" ); document.write( " 6 + 4 = 10 hrs
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\n" ); document.write( "could you follow this OK?\r
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