SOLUTION: #80 Air Traffic Control. An air traffic controller spots two planes at the same altitude flying toward each other. Their flight paths form a right angle at point P. One plae is 15

Question 182170This question is from textbook College Algebra The Graphing Approach
: #80
Air Traffic Control. An air traffic controller spots two planes at the same altitude flying toward each other. Their flight paths form a right angle at point P. One plae is 150 miles from point P and is moving at 450 miles per hour. The other plane is 200 miles from point P and is moving at 450 miles per hour. Write the distance x between the planes as a function of time t.
Thanks for your help.This question is from textbook College Algebra The Graphing Approach

Answer by vleith(2517) (Show Source):
You can put this solution on YOUR website!
Assume the two planes are heading 'towards P'. For now, let's not get too wound up about the x and y aspects. We'll always 'know' the two places are at right angles to each other.
First let's create two equations that represent the 'location' of each plane.
Plane1Location = 150 - 450(t) (on the x axis)
Place2Location = 200 - 450(t) (on the y axis)
The distance between them ends up being the hypotenuse of the triangle with sides that are represented by Plane1Location and Place2Location.

Expand the right side, simplify and the take the square root to get the function c(t) over time.