Question

There is a church tower 150 feet tall and another catholic tower at a distance of 350 feet from it which is 200 feet tall. There is one each bird sitting on top of both the towers. They fly at a constant speed and time to reach a grain in between the towers at the same time. At what distance from the church is the grain?

Answer 1

Answer:

Distance from the church is 200 ft

Explanation:

As Birds fly with a constant speed & Reach at same time

so distance covered by both is same

Let say Distance of grain  is x from  150 ft tall

then 350 - x from 200 ft tall

Distance covered by both birds are equal

150² + x² = (350 -x)² + 200²

=> 22500 + x² = 122500 + x² - 700x + 40000

=> 700x = 140000

=> x = 200

Distance from the church is 200 ft

Answer 2

Answer:

Distance of the grain from the church tower, x = 200 m

Step by Step Explanation:

Height of the church tower = 150 feet

Height if the catholic tower = 200 feet

Distance between the towers = 350 feet

Now,

As they reach the grain at the same time the Speed and the Time taken by them is same and therefore the Distance.

So,

Let us say that the distance of the grain from the church tower is = x feet

So,

Using the Pythagoras theorem in the two triangles we get,

$(150)^{2}+x^{2}=Distance$

Also,

$(200)^{2}+(350-x)^{2}=Distance$

So, on equating the both we get,

$(200)^{2}+(350-x)^{2}=(150)^{2}+x^{2}$

So,

$(200)^{2}+(350-x)^{2}=(150)^{2}+x^{2}\\40000+122500+x^{2}-700x=22500+x^{2}\\700x=140000\\x=200\ m$

Therefore, the distance of the grain from the church tower is, x = 200 m.