SOLUTION: A cathedral tower 200 feet high is 250 feet from a chruch tower 150 feet high. On top of each tower is a pigeon. The two pigeons fly off at the same time and at the same speed dire

Question 588920: A cathedral tower 200 feet high is 250 feet from a chruch tower 150 feet high. On top of each tower is a pigeon. The two pigeons fly off at the same time and at the same speed directly to some grain on the level straight road between the towers. The pigeons reach the grain at the same time.
How far is the grain from the foot of the cathedral tower?
I tried to solve it myself and when that failed i turned to the internet. when i look at the work shown however it just shows : 200^2+x^2=150^2-500x+x^2 etc.
where does the 500x come from ?
Answer by ankor@dixie-net.com(15646) (Show Source):
You can put this solution on YOUR website!
A cathedral tower 200 feet high is 250 feet from a church tower 150 feet high.
On top of each tower is a pigeon.
The two pigeons fly off at the same time and at the same speed directly to some grain on the level straight road between the towers.
The pigeons reach the grain at the same time.
How far is the grain from the foot of the cathedral tower?
:
I guess we assume each pigeon flies at the same speed.
:
The two towers form a right triangle, the two hypotenuses are the path of the pigeons to the grain and are equal
:
Let x = distance to the grain from the cathedral
then
(250-x) = distance to the grain from the church tower
:
Cathed hypot = Church hypot
x^2 + 200^2 = (250-x)^2 + 150^2
FOIL (250-x)(250-x)
x^2 + 40000 = 62500 - 500x + x^2 + 22500
Combine like terms
x^2 - x^2 + 500x = 62500 + 22500 - 40000
500x = 45000
x =
x = 90 ft from the cathedral
:
The 500x comes when you FOIL (250-x)(250-x)
:
:
Check by finding the hypotenuses, they should be equal if we did this right
h1 =
h1 = 219.3 ft
:
Distance from church: 250-90 = 160
h2 =
h2 = 219.3 ft, our solution is correct