SOLUTION: 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 he

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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?
Found 2 solutions by macston, lwsshak3:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let r=the rate of Flight 237
Between noon and 3:00pm (3 hours), Flight 237 travels 3hrs(r) miles.
Flight 875 travels 3hrs(r-40mph)
These two distances form a right triangle with hypotenuse=600 miles.
%283hrs%28r%29%29%5E2%2B%283hrs%28r-40%29%29%5E2=600%5E2
%289r%5E2%29%2B%283r-120%29%5E2=360000
9r%5E2%2B9r%5E2-720r%2B14400=360000
18r%5E2-720r-345600=0
r%5E2-40r-19200=0
%28r-160%29%28r%2B120%29=0
r-160=0 or r%2B120=0
r=160 or r=-120
The rate of Flight 237 was 160 mph.
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CHECK:
The rate of Flight 237 was 160 mph, so its distance was 480 miles.
The rate of Flight 875 was 120 mph, so its distance was 360 miles .
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%28480mi%29%5E2%2B%28360mi%29%5E2=%28600mi%29%5E2
230400mi%5E2%2B129600mi%5E2=360000mi%5E2
360000mi%5E2=360000mi%5E2

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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?
***
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