a maths puzzle pls solve it?

Question

.There are two towers A and B. Their heights are 200ft and 150ft respectively and the foot of the towers are 250ft apart. Two birds on top of each tower fly down with the same speed and meet at the same instant on the ground to pick a grain. What is the distance
between the foot of tower A and the grain?

Answer 1

Let a = 200 = height of Tower A
Let g = the number of feet from the base of Tower A to the grain.
The distance flown by Bird A is:
√(200² + g²)

Let b = 150 = height of Tower B
Since the distance between the bases of the towers is 250 feet, and "g" is the distance from the base of Tower A to the grain, the distance from the base of Tower B to the grain is (250 - g).
The distance flown by Bird B is:
√[150² + (250 - g)²]

Since they arrived at the same time and traveled at the same speed, the two distances are equal.

√(200² + g²) = √[150² + (250 - g)²]
Squaring both sides,
200² + g² = 150² + (250 - g)²
40000 + g² = 22500 + (62500 - 500g + g²)
40000 + g² = 85000 - 500g + g²
Adding (-g² + 500g - 40000) to both sides,
500g = 45000
g = 45000 / 500 = 90

The grain is 90 feet from the bottom of Tower A.

Answer 2

To start, draw a simplified picture. Draw a vertical line for tower A on the left, and label it "200 ft." Draw another vertical line for tower B on the right (make sure their bases line up), and label it "150 ft." Connect the bases with a horizontal line, and label it "250 ft.

Now, somewhere on that line, mark a point. That'll be where the grain is. We'll call the distance from the foot of Tower A to that point "x."

There are two key things to realize:

(1) The distance from the top of a tower to that point can be found using the Pythagorean Theorem.
(2) Since both birds fly the same speed, both leave at the same time, and both meet at the same time, they must fly the same distance. In other words, the distance from the top of A to the grain is the same as the distance from the top of B to the grain.

Draw dotted lines from the tops of both towers to the grain. See the two right triangles? With the dotted lines for hypotenuses?

The base of the one on the left (the one that uses Tower A) has length x, of course... and the base of the one on the right has length (250 - x).

For the hypotenuse on the left, which we might call c, we have
c^2 = 200^2 + x^2

For the hypotenuse on the right, which we might call d, we have
d^2 = 150^2 + (250 - x)^2

But we know that c = d (see point #2 above), which means c^2 = d^2. So:

200^2 + x^2 = 150^2 + (250 - x)^2

Let's solve this for x.

40000 + x^2 = 22500 + (62500 - 500x + x^2)

Simplifying,

40000 + x^2 = 85000 - 500x + x^2

Subtracting x^2 from both sides, we get

40000 = 85000 - 500x

Subtracting 85000 from both sides,

-45000 = -500x

Finally, dividing both sides by 500 gives

90 = x

So it appears the grain is 90 feet from the base of Tower A. Does that work? Let's check: by the Pythagoreon Theorem, the grain will be √(200^2 + 90^2) = √48100 feet from the top of Tower A, and √(150^2 + 160^2) = √48100 feet from the top of Tower B. We don't actually need to work out √48100 to see that the distances match. :)

Hope that clears it up for ya! :)

Answer 3

If the birds fly down with the same speed and meet at the same time it means they cover the same distance. Call it z.

Also call distance first tower - grain --> x
second - grain --> y
x+y=250

z^2 = 200^2 + x^2 and z^2 = 150^2 +y^2
x+y=250
x^2-y^2 = 150^2 - 200 ^2

250*(x-y) = -50 * 350

x+y = 250
x-y = -70

2x =180 x=90 feet

Answer 4

90 feet from tower A and 160 feet from tower B. Where would we be without Joe Pythagoras!

Answer 5

We're looking at 2 right triangles ABC and A'B'C'

B = 200 ft, B' = 150 ft
C=C'
A+A'=250

plus pythagorean's

so:
A^2+B^2=A'^2+B'^2
or solving for A
A^2-(250-A)^2= 200^2-150^2 ; or
500A-62500=17500
A=160

Therefore, 160 feet

Answer 6

can't you not answer that question because it does not tell you where the grain is. there is no way to determin that answer when it asks you how far the grain is from the foot of the building....

i think

Answer 7

90 feet

Answer 8

My guess is 187.5 feet from Tower A.

Answer 9

50 feets!

Answer 10

90 feet. Curious why are you asking this simple question...