A jet flies with the wind at 1100 km/hr and 750 km/hr against the same wind. Find the rate of the wind and the speed of the plane

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To find the rate of the wind and the speed of the plane, we can set up a system of equations based on the given information.

Let's denote the speed of the plane as "x" and the rate of the wind as "y".

When the plane flies with the wind, its effective speed is the sum of its own speed and the speed of the wind. So, the speed of the plane when flying with the wind is x + y.

Similarly, when the plane flies against the wind, its effective speed is the difference between its own speed and the speed of the wind. So, the speed of the plane when flying against the wind is x - y.

According to the given information, the plane's speed when flying with the wind is 1100 km/hr, which we can write as:

x + y = 1100 -- Equation 1

And the plane's speed when flying against the wind is 750 km/hr, which we can write as:

x - y = 750 -- Equation 2

To solve this system of equations, we can use the method of elimination or substitution. In this case, let's solve it by elimination.

By adding Equation 1 and Equation 2, we can eliminate the variable "y":

(x + y) + (x - y) = 1100 + 750
2x = 1850

Dividing both sides of the equation by 2, we get:

x = 925

So, the speed of the plane (without the wind) is 925 km/hr.

Now, to find the rate of the wind, we can substitute the value of x back into Equation 1 or Equation 2:

x + y = 1100

Substituting x = 925, we have:

925 + y = 1100

Subtracting 925 from both sides of the equation, we get:

y = 1100 - 925

y = 175

Therefore, the rate of the wind is 175 km/hr.

In summary, the speed of the plane is 925 km/hr and the rate of the wind is 175 km/hr.