document.write( "Question 972570: At 12-noon flight 237 leaves Chicago headed due south and traveling at a rate of r miles per hour. At 12-noon a second flight, flight 875, left Chicago from a different runway headed due east and traveling 40 miles per hour slower than flight 237. At 3:00pm the planes are 600 miles apart. How fast is flight 237 traveling? \n" ); document.write( "

Algebra.Com's Answer #594878 by macston(5194) $\"\"$ $\"About$

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\n" ); document.write( "Let r=the rate of Flight 237
\n" ); document.write( "Between noon and 3:00pm (3 hours), Flight 237 travels 3hrs(r) miles.
\n" ); document.write( "Flight 875 travels 3hrs(r-40mph)
\n" ); document.write( "These two distances form a right triangle with hypotenuse=600 miles.
\n" ); document.write( " $\"%283hrs%28r%29%29%5E2%2B%283hrs%28r-40%29%29%5E2=600%5E2\"$
\n" ); document.write( " $\"%289r%5E2%29%2B%283r-120%29%5E2=360000\"$
\n" ); document.write( " $\"9r%5E2%2B9r%5E2-720r%2B14400=360000\"$
\n" ); document.write( " $\"18r%5E2-720r-345600=0\"$
\n" ); document.write( " $\"r%5E2-40r-19200=0\"$
\n" ); document.write( " $\"%28r-160%29%28r%2B120%29=0\"$
\n" ); document.write( " $\"r-160=0\"$ $\"or\"$ $\"r%2B120=0\"$
\n" ); document.write( " $\"r=160\"$ $\"or\"$ $\"r=-120\"$
\n" ); document.write( "The rate of Flight 237 was 160 mph.
\n" ); document.write( ".
\n" ); document.write( "CHECK:
\n" ); document.write( "The rate of Flight 237 was 160 mph, so its distance was 480 miles.
\n" ); document.write( "The rate of Flight 875 was 120 mph, so its distance was 360 miles .
\n" ); document.write( ".
\n" ); document.write( " $\"%28480mi%29%5E2%2B%28360mi%29%5E2=%28600mi%29%5E2\"$
\n" ); document.write( " $\"230400mi%5E2%2B129600mi%5E2=360000mi%5E2\"$
\n" ); document.write( " $\"360000mi%5E2=360000mi%5E2\"$
\n" ); document.write( " \n" ); document.write( "

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