document.write( "Question 33306: 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 10 hours, what is the planes's speed in still air. \n" ); document.write( "

Algebra.Com's Answer #19710 by Paul(988) $\"\"$ $\"About$

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Plane total distance = 720 miles:
\n" ); document.write( "With the wind the plane speed is: x+30
\n" ); document.write( "Against the wind: x-30
\n" ); document.write( "Total time of them both = 10h
\n" ); document.write( "equation:
\n" ); document.write( " $\"720%2F%28x-30%29%2B720%2F%28x%2B30%29=10\"$
\n" ); document.write( "720[(x-30)+(x+30)]=10[(x-30)(x+30)]
\n" ); document.write( "720(2x)=10(x^2-900)
\n" ); document.write( "10x^2-9000-1440x=0
\n" ); document.write( "x^2-144x-900=0
\n" ); document.write( " $\"x%5E2-144x-900=0\"$
\n" ); document.write( "Use quadratic formula: $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "in $\"ax%5E2%2Bbx%2Bc\"$ a=1, b=-144, c=-900
\n" ); document.write( " $\"x=%28-%28-144%29%2B-sqrt%28%28-144%29%5E2-4%281%29%28-900%29%29%29%2F+2+%2A+%281%29%29\"$ -->DIVIDE BY 2
\n" ); document.write( " $\"x=%28144%2B-sqrt%2824336%29%29%2F+2\"$ --->
\n" ); document.write( " $\"x=%28144%2B-156%29%2F%282%29\"$
\n" ); document.write( "Add:
\n" ); document.write( " $\"x=144%2B156%2F%282%29\"$
\n" ); document.write( "x=150\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Hence the speed of the plane in still air is 150mi/h.
\n" ); document.write( "Paul.\r
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