document.write( "Question 213913: Two planes leave simultaneously from the same airport, one flying due east and the other due south. The eastbound plane is flying 100 miles per hour faster than the southbound plane. After 4 hours the planes are 3080 miles apart. Find the speed of each plane. (Use 1 decimal place.) \n" ); document.write( "

Algebra.Com's Answer #161647 by checkley77(12844) $\"\"$ $\"About$

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4(X+100)^2+4X^2=3080^2
\n" ); document.write( "4(X^2+200X+10,000)+4X^2=9,486,400
\n" ); document.write( "4X^2+800X+40,000+4X^2=9,486,400
\n" ); document.write( "8X^2+800X+40,000-9,486,400=0
\n" ); document.write( "8X^2+800X-9,446,400=0
\n" ); document.write( "8(X^2+100X-1,180,800)=0
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "X=(-100+-SQRT[100^2-4*1*-1,180,800])/281
\n" ); document.write( "X=(-100+-SQRT[10,000+4,723,200])/2
\n" ); document.write( "X=(-100+-SQRT4,733,200)/2
\n" ); document.write( "X=(-100+-2,175.5918)/2
\n" ); document.write( "X=(-100+2,175.5918)/2
\n" ); document.write( "X=2,075.5918/2
\n" ); document.write( "X=1,037.8 ANS. FOR THE SLOWER PLANE.
\n" ); document.write( "1,037.8+100=1,137.8 ANS. FOR THE FASTER PLANE.
\n" ); document.write( "PROOF:
\n" ); document.write( "4(1,137.8)^2+4*1,037.8^2=3080^2
\n" ); document.write( "4*1,294,588.8+4*1,077,028.8=9,486,400
\n" ); document.write( "5,178,355.2+4,308,115.2=9,486,400
\n" ); document.write( "9,486,400~9,486,400
\n" ); document.write( " \n" ); document.write( "

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