A jet takes the same time to travel 2500km with the wind as it does to travel 1900 km against the wind. If its speed relative to the air is 450km/hr, what is the speed of the wind?

"same time", so we form an equation by setting the times equal to each other.

2500/(450+x) = 1900/(450-x)

cross multiply and solve for x

To solve this problem, we need to set up an equation based on the given information.

Let's assume the speed of the jet is x km/hr and the speed of the wind is y km/hr.

When the jet is traveling with the wind, its effective speed is (x + y) km/hr. Distance = Speed × Time, so we can write the following equation for traveling with the wind:

2500 km = (x + y) km/hr × T1 hr ----(1)

Similarly, when the jet is traveling against the wind, its effective speed is (x - y) km/hr. Using the same logic, we can write the equation for traveling against the wind:

1900 km = (x - y) km/hr × T2 hr ----(2)

From the given information, we know that the jet's speed relative to the air is 450 km/hr, which means x = 450 km/hr. Now we can substitute this value into equations (1) and (2):

2500 km = (450 km/hr + y km/hr) × T1 hr ----(3)

1900 km = (450 km/hr - y km/hr) × T2 hr ----(4)

We need to find the value of y, which represents the speed of the wind. To do that, we need to eliminate the variables T1 and T2 from equations (3) and (4).

We can rearrange equation (3) to solve for T1:

T1 = 2500 km / (450 km/hr + y km/hr)

Now, rearrange equation (4) to solve for T2:

T2 = 1900 km / (450 km/hr - y km/hr)

Since T1 and T2 are the same, we can set them equal to each other:

2500 km / (450 km/hr + y km/hr) = 1900 km / (450 km/hr - y km/hr)

To simplify the equation, we can cross-multiply:

2500 km * (450 km/hr - y km/hr) = 1900 km * (450 km/hr + y km/hr)

Now, expand and simplify:

1125000 km/hr - 2500 km * y = 855000 km/hr + 1900 km * y

Rearrange the equation to isolate y:

2500 km * y + 1900 km * y = 1125000 km/hr - 855000 km/hr

4400 km * y = 270000 km/hr

y = 270000 km/hr / 4400 km

y ≈ 61.36 km/hr

Therefore, the speed of the wind is approximately 61.36 km/hr.