An airplane flies 1050 km with the wind. In the same amount of time, it can fly 750 km against the wind. The speed of the plane in the still air is 200 km/h. Find the speed of the wind.

To find the speed of the wind, we can use the concept of relative velocity. Let's assume the speed of the wind is denoted by 'w' km/h.

When the plane flies with the wind, its speed with respect to the ground is the sum of the speed of the plane and the speed of the wind. Similarly, when the plane flies against the wind, its speed with respect to the ground is the difference between the speed of the plane and the speed of the wind.

Given that the speed of the plane in still air is 200 km/h, we can now calculate the speed of the plane with the wind and against the wind.

Speed of the plane with the wind = Speed of the plane in still air + Speed of the wind
= 200 km/h + w km/h
= (200 + w) km/h

Speed of the plane against the wind = Speed of the plane in still air - Speed of the wind
= 200 km/h - w km/h
= (200 - w) km/h

Now, we can use the given information that the plane takes the same amount of time to travel 1050 km with the wind and 750 km against the wind. This means that the time taken for both scenarios is equal.

Time taken to fly with the wind = Time taken to fly against the wind

Distance/Speed = Distance/Speed

1050 km / (200 + w) km/h = 750 km / (200 - w) km/h

To solve this equation, we can cross-multiply and simplify:

1050 km * (200 - w) km/h = 750 km * (200 + w) km/h

Dividing both sides by 50 km/h:

21 km * (200 - w) = 15 km * (200 + w)

Expanding both sides:

4200 km - 21w = 3000 km + 15w

Grouping like terms:

-21w - 15w = 3000 km - 4200 km

-36w = -1200 km

Dividing both sides by -36:

w = -1200 km / -36

w ≈ 33.33 km/h

Therefore, the speed of the wind is approximately 33.33 km/h.