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?
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both planes have been flying for 3 hours(travel time)
let r=speed of flight 237
r-40=speed of flight 875
distance =speed*travel time
..
3r=distance traveled by flight 237(1 leg of right triangle)
3(r-40)distance traveled by flight 875(other leg of right triangle)
600=hypotenuse of right triangle
By the Pythagorean Theorem:
600^2=9r^2+9(r-40)^2
600^2=9r^2+9(r^2-80r+1600)
360000=9r^2+9r^2-720r+14400)
18r^2-720r-345600=0
divide by 18
r^2-40r-19200=0
(r-160)(r+120)=0
r=160
How fast is flight 237 traveling? 160 mph