Math word problem! 5 stars!

There are two flagpoles 100 meters apart. The pole to the right is 40 meters tall, and the left one is 30 meters tall. Two birds fly down from each pole, and land on the ground at the same time. How far are the birds from the poles when they reach the ground?

5 stars for best answer!!

Thanks in advance :-)

I'm assuming that you mean the birds fly at the same speed.

With that assumption, what you're looking for is that the hypotenuses of the two right triangles formed by the paths of the birds flying off their respective poles be equal. Those equal lengths, coupled with the assumption that the birds fly at the same speed implies that the birds will land simultaneously.

Let's call the distance of the first bird from it's flagpole l1, and the distance of the second bird l2. The distance between them will then be D = 100-l1-l2.

Now for the first bird, it must be true that

l1^2+30^2 = H^2 (where H is the hypotenuse in question)

And it must be true for the second bird that

l2^2 +40^2 = H^2

Equating, we find

l1^2 - l2^2 = 40^2 - 30^2

OR

l1^2 - l2^2 = 700

Now substitute from the distance equation for l2

l1^2 - (100-l1-D)^2 = 700

Expanding the lhs

-D^2+200*D-2*D*l+200*l-10000 = 700

Or

D^2-(200+2*l1)*D-200*l1+10700 = 0


You can now use the quadratic equation to find how the distance between the birds depends on the distance from the flagpole that the first one lands. In other words, there's not just one answer but a series of answers depending on the speed of the birds. If you had specified a speed for the birds there would only be a single answer.