2 airplanes start at the same time from airports 500 km apart. Each flies with an airspeed of 200 km/hr toward the other airport. One reaches its airport half an hour before the other plane reaches the other airport. How fast is the wind blowing?

let the windspeed be x km/h

time going with the wind = 500/(200+x)
time going against the wind = 500(200-x)
the difference in those times = 1/2 hr

500/(200-x) - 500/(200+x) = 1/2
times 2(200-x)(200+x)

1000(200+x) - 1000(200-x) = (200-x)(200+x)
200000 + 1000x - 2000000 +1000x = 40000 - x^2
x^2 + 2000x - 40000 = 0
using the quadratic formula, I got
x = 19.8 or an unreasonable 2nd answer

the windspeed is 19.8 km/h

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To determine the speed of the wind, let's break down the problem and work through it step by step.

Let's assume that the speeds of the two airplanes are constant, and let's call the speed of the first plane A and the speed of the second plane B. Since they are both flying towards each other, we can consider their combined speed as the sum of their individual speeds, which is A + B.

The distance between the two airports is 500 km. Let's represent the time it takes for the second plane to reach the other airport as t hours. Since the first plane reaches its airport half an hour earlier than the second, we can represent the time it takes for the first plane to reach its airport as (t + 0.5) hours.

Now, we can use the formula: Distance = Speed x Time to help solve the problem.

For the first plane, we have:
Distance = (A + B) * (t + 0.5)

For the second plane, we have:
Distance = (A + B) * t

Since both planes are traveling the same distance, we can equate the two equations:

(A + B) * (t + 0.5) = (A + B) * t

Next, we can simplify the equation by canceling out (A + B) on both sides:

t + 0.5 = t

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

0.5 = 0

This equation is not possible, and therefore, we have an error in our assumptions. It is not possible for one plane to reach its destination half an hour earlier than the other plane when they are both traveling at a constant speed towards each other.

Therefore, we cannot determine the speed of the wind based on the provided information.