Answer: the speed of the wind is 50 mph.
Explanation:
Let x represent the speed of the wind.
The plane has a cruising speed of 250 mph when there is no wind. At this speed, the plane flew 300 miles with the wind. This means that the total speed at which the plane flew was (250 + x) mph
Time = distance/speed
The time spent by the plane in flying 300 miles is
300/(250 + x)
In the same amount of time, it flew 200 miles against the wind. This means that the total speed at which the plane flew was (250 - x) mph
Time = distance/speed
The time spent by the plane in flying 200 miles is
200/(250 - x)
Since the time is the same, then
300/(250 + x) = 200/(250 - x)
Cross multiplying, it becomes
200(250 + x) = 300(250 - x)
50000 + 200x = 75000 - 300x
200x + 300x = 75000 - 50000
500x = 25000
x = 25000/500
x = 50