The problem states that the paths of the two planes form a right triangle, therefore this means that the distance between the two is the hypotenuse. Given that information, we can use the hypotenuse formula for finding the distance formula:
c^2 = a^2 + b^2 ---> 1
Where c is the hypotenuse, in this case the distance between the two planes.
First let us find the value of a. We know that one plane is 150 miles from point P and this distance is decreasing by a rate of 450 miles per hour, therefore a is:
a = 150 – 450 t ---> 2
We also know that the other plane is 200 miles away and this distance decreases by a rate of 450 miles per hour also, therefore b is:
b = 200 – 450 t ---> 3
Substituting equations 2 and 3 to 1:
c^2 = (150 - 450 t)^2 + (200 – 450 t)^2
c^2 = 22500 – 135000t + 202500t^2 + 40000 – 180000t + + 202500t^2
c^2 = 405,000 t^2 – 315,000 t + 62,500 (ANSWER)
