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

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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) About Me  (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.
+a%5E2+%2B+b%5E2+=+c%5E2+
+%282%28x%2B100%29%29%5E2+%2B+%282x%29%5E2+=+1500%5E2+
+%282x%2B200%29%5E2+%2B+%282x%29%5E2+=+1500%5E2+
Foil the first term out
+%284x%5E2%2B800x%2B40000%29+%2B+%282x%29%5E2+=+1500%5E2+
Work the 2nd tem
+%284x%5E2%2B800x%2B40000%29+%2B+4x%5E2+=+1500%5E2+
work the right side
+4x%5E2+%2B+800x+%2B+40000+%2B+4x%5E2+=+2250000+
combine like terms on the left
+8x%5E2+%2B+800x+%2B+40000+=+2250000+
subtract 2250000 from both sides
+8x%5E2+%2B+800x+-+2246000+=+0+
factor out an 8 from all terms
+8%28x%5E2+%2B+100x+-+2210000%29+=0+
divide by 8
+x%5E2+%2B+100x+-+276250+=0+
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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B100x%2B-276250+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28100%29%5E2-4%2A1%2A-276250=1115000.

Discriminant d=1115000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-100%2B-sqrt%28+1115000+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28100%29%2Bsqrt%28+1115000+%29%29%2F2%5C1+=+477.967802048572
x%5B2%5D+=+%28-%28100%29-sqrt%28+1115000+%29%29%2F2%5C1+=+-577.967802048572

Quadratic expression 1x%5E2%2B100x%2B-276250 can be factored:
1x%5E2%2B100x%2B-276250+=+1%28x-477.967802048572%29%2A%28x--577.967802048572%29
Again, the answer is: 477.967802048572, -577.967802048572. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B100%2Ax%2B-276250+%29

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