SOLUTION: Two birds start flying from the tops of two towers 50 feet apart; one tower is 30 feet high and the other 40 feet high. Starting at the same time and flying at the same rate, the b

Question 1029394: Two birds start flying from the tops of two towers 50 feet apart; one tower is 30 feet high and the other 40 feet high. Starting at the same time and flying at the same rate, the birds reach a fountain between the bases of the towers at the same moment. How far is the fountain from each tower
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
You have to draw this.
The towers are 50 feet apart. To reach a spot between them, the birds have to fly from the top to a point between them. There is a right triangle, and the hypotenuses have to be equal.
The bird on the shorter triangle is part of a triangle with the tower 30 and the distance x to the fountain. They square to 900 + x^2.
The other bird on the 40 foot tower has a distance to the fountain on the ground of 50-x, because the towers are 50 feet apart.
That squares to 2500-100x+x^2.
These must be equal.
2500-100x+x^2+1600=900+x^2
4100-100x=900
-100x=-3200
x=32 feet from the shorter tower and 18 feet from the larger tower.
Therefore 30^2+32^2=40^2+18^2

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