A plane has a cruising speed of 250 mph when there is no wind. At this speed, the plane flew 300 miles with the wind in the same amount of time it flew 200 miles against the wind. Find the speed of the wind.

Answer: the speed of the wind is 50 mph.

Step-by-step 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