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Two airplanes begin 1000 miles apart and fly along lines that intersect at a right angle.
\n" ); document.write( "One plane flies an average of 100 MPH faster than the other.
\n" ); document.write( "If the planes meet after 2 hours, how fast do the airplanes fly?
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\n" ); document.write( "the distance between the planes represent the hypotenuse of the right triangle
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\n" ); document.write( "Let s = speed of the slower plane
\n" ); document.write( "then
\n" ); document.write( "(s+100) = speed of the faster plane
\n" ); document.write( ":
\n" ); document.write( "The distance to the intersection can we written:\r
\n" ); document.write( "\n" ); document.write( "2s for the slower plane; one leg of the right triangle
\n" ); document.write( "2(s+100) for the faster which is: (2s + 200); the other leg of the right triangle
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\n" ); document.write( "(2s)^2 + (2s+200)^2 = 1000^2
\n" ); document.write( ":
\n" ); document.write( "4s^2 + (4s^2 + 800s + 40000) = 1000000
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\n" ); document.write( "8s^2 + 800s + 40000 - 1000000 = 0
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\n" ); document.write( "8s^2 + 800s - 960000 = 0
\n" ); document.write( "Simplify divide by 8
\n" ); document.write( "s^2 + 100s - 120000 = 0
\n" ); document.write( "Factor this to
\n" ); document.write( "(s - 300)(s + 400) = 0
\n" ); document.write( "Positive solution
\n" ); document.write( "s = 300 mph is the slow plane
\n" ); document.write( "and
\n" ); document.write( "300 + 100 = 400 mph is the fast plane
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\n" ); document.write( "Check this using a^2 + b^2 = c^2
\n" ); document.write( "600^2 + 800^2 = 1000^2
\n" ); document.write( "360000 + 640000 = 1000000 \n" ); document.write( "