SOLUTION: Two planes leave simultaneously from the same airport, one flying due north and one flying due east. The northbound plane is flying 50 mph faster than the eastbound plane. After 3

Question 487176: Two planes leave simultaneously from the same airport, one flying due north and one flying due east. The northbound plane is flying 50 mph faster than the eastbound plane. After 3 hours they are 2440 miles apart. Find the speed of each plane.
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
(3n-150)2+(3n)2=(2440)2
9n2-900n+22500+9n2=5953600
18n2-900n-5931100=0
9n2-450n-2965550=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=106962300 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 599.569887442386, -549.569887442386. Here's your graph:

Throwing out the negative answer, we get the speeds of the planes to be approximately 600 mph for the northbound plane, and 550 mph for the eastbound plane..
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