document.write( "Question 24178: A plane flies 720 mi 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 the air? \n" ); document.write( "

Algebra.Com's Answer #12864 by Paul(988) $\"\"$ $\"About$

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Let the plane's speed be x
\n" ); document.write( "Agianst the headwind = x-30
\n" ); document.write( "With the headwind = x+30
\n" ); document.write( "total time = 10h\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"720%2Fx-30+%2B+720%2Fx%2B30+=+10\"$
\n" ); document.write( "720[(x-30)+(x+30)]=10[(x-30)(x+30)] --> simplify
\n" ); document.write( " $\"720%5B2x%5D=10%5Bx%5E2-900%5D\"$
\n" ); document.write( " $\"1440x=10x%5E2-9000\"$
\n" ); document.write( "Quardrtic equation: $\"10x%5E2-1440x-9000+=+0\"$ --> divide the equation by 10
\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( " $\"x=-%28-144%29%2B-sqrt%28%28-144%29%5E2-4%281%29%28-900%29%29%29%2F+2+x+%281%29%29\"$ -->DIVIDE BY 2
\n" ); document.write( " $\"x=144%2B-sqrt%2824336%29%29%2F+2\"$ ---> DIVIDE by 2.
\n" ); document.write( " $\"x=144%2B-156%2F%282%29\"$
\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 sir is 150mi/h.
\n" ); document.write( "Paul.
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