SOLUTION: Two airplanes leave simultaneously from an airport. One flies due south; the other flies due east at a rate 20 mph faster than the first airplane. After 1.5 hours, radar indicate

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Question 598103: Two airplanes leave simultaneously from an airport. One flies due south; the other flies due east at a rate 20 mph faster than the first airplane. After 1.5 hours, radar indicates that the airplanes are 450 miles apart. What is the ground speed of each airplane?
Please help - I am so lousy at word problems and stuggle with how to set up and solve. My instructor requires that we show all the work. So please help me with this homework problem step by step as I need to really understand how to pull out necessary information, then set up the equation to be solved. You are a lifesaver... Thank you so much!!!

Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
Two airplanes leave simultaneously from an airport. One flies due south; the other flies due east at a rate 20 mph faster than the first airplane. After 1.5 hours, radar indicates that the airplanes are 450 miles apart. What is the ground speed of each airplane?
.
Let x = ground speed of slower plane
then
x+20 = ground speed of faster plane
.
Because of the directions the two planes are flying, they form "right angle" (90 degrees). Therefore, you can use Pythagorean Theorem to solve:
applying the distance formula: d=rt
(1.5x)^2 + (1.5(x+20))^2 = 450^2
2.25x^2 + (1.5x+30)^2 = 202500
2.25x^2 + (1.5x+30)(1.5x+30) = 202500
2.25x^2 + 2.25x+90x+900 = 202500
4.5x^2+90x-201600 = 0
.5x^2+10x-22400 = 0
apply the quadratic formula to solve, which gives us:
x = {201.8962, -221.8962}
throw out the negative solution (extraneous) leaving
x = 202 mph (slower plane)
.
faster plane:
x+20 = 202+20 = 222 mph
.
details of quadratic follows:
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=44900 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 201.896201004171, -221.896201004171. Here's your graph:
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