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

Question 991509: 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?
Answer by ankor@dixie-net.com(22740) (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.
Therefore
(r-40) = rate of the flt 875
:
At 3:00pm the planes are 600 miles apart.
travel time of both planes is 3 hr
therefore
3r = dist traveled by flt 237
3(r-40) = (3r-120) = dist traveled by flt 875
:
How fast is flight 237 traveling?
:
They are flying at right angles to one another, this is a pythag problem
a^2 + b^2 = c^2, where
a = 3r
b = 3(r-40)
c = 600
(3r)^2 + (3r-120)^2 = 600^2
9r^2 + (9r^2 - 720r + 14400) = 360000
18r^2 - 720r + 14400 - 360000 = 0
18r^2 - 720r - 345600 = 0
simplify, divide by 18
r^2 - 40r - 19200 = 0
you can use the quadratic formula. a=1; b=-40; c=-19200, but it will factor to
(r+120)(r-160) = 0
The positive solution
r = 160 mph, flt 237
:
;
:
Check this find the dist each traveled
flt 237: 3*160 = 480 mi
flt 875: 3*120 = 360 mi
Enter in your calc
resulting in 600

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