SOLUTION: two planes leave simultaneously from the same airport, one flying due east and the other due south. The eastbound plane is flying 100 miles per hour faster than the southboun plane

Question 35047This question is from textbook
: two planes leave simultaneously from the same airport, one flying due east and the other due south. The eastbound plane is flying 100 miles per hour faster than the southboun plane. After 2 hours the planes are 1500 miles apart - Find the speed of each plane -
use d=rt
my try
[d=r+100(2)]-[d=r(2)]=1500
please help!!!! This question is from textbook

Answer by Cintchr(481) (Show Source): You can put this solution on YOUR website!
For this one .... think triangles :)
Eastbound plane (a) : 2(x+100)
Southbound plane (b) : 2x
The distance between them (c) : 1500
The starting point, and the points where they are after 2 hours, form a right triangle where the distance between them is the hypotenuse.

Foil the first term out

Work the 2nd tem

work the right side

combine like terms on the left

subtract 2250000 from both sides

factor out an 8 from all terms

divide by 8

This does NOT factor out all nice and pretty ... and even when using the quadratice formula ... we get a NASTY decimal number .....

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=1115000 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 477.967802048572, -577.967802048572. Here's your graph:

But as you can see with the Quadratic equation ... it comse out to be roughly 477 and 577 miles per hour.

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