SOLUTION: Two airplanes depart simultaneously from an airport. One flies due south; the other flies due east at a rate 30 mph faster than that of the first airplane. After 3 hours, rada

Question 576301: Two airplanes depart simultaneously from an airport. One flies due south; the other flies due
east at a rate 30 mph faster than that of the first airplane. After 3 hours, radar indicates that
the airplanes are 450 miles apart. What is the ground speed of each airplane
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two airplanes depart simultaneously from an airport.
One flies due south; the other flies due east at a rate 30 mph faster than that of the first airplane.
After 3 hours, radar indicates that the airplanes are 450 miles apart.
What is the ground speed of each airplane.
:
let s = speed of the southbound airplane
then
(s+30) = speed of the eastbound
:
dist = time * speed, therefore
3s = distance traveled by the southbound plane
and
3(s+30) = distance traveled by the eastbound plane
:
This is a right triangle problem: a^2 + b^2 = c^2, where
a = 3s
b = 3(s+30)
c = 450
:
(3s)^2 + (3(s+30))^2 = 450^2
9s^2 + (3s+90)^2 = 202500
9s^2 + 9s^2 + 270s + 270s + 8100 - 202500 = 0
18s^2 + 540s - 194400 = 0
simplify, divide by 18
s^2 + 30s - 10800 = 0
you can use the quadratic formula to find s, but this will factor to:
(s+120)(s-90) = 0
the positive solution is all we want here
s = 90 mph, speed of the southbound plane
then
90+30 = 120 mph, speed of the eastbound
:
:
Check this out on your calc: enter results 450

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