A plane has an airspeed of 190 miles per hour and a heading of 24.0°. The ground speed of the plane is 214 miles per hour, and its true course is in the direction of 40.0°. Find the speed and direction of the air currents, assuming they are constants. (Round your answers to one decimal place.)

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To find the speed and direction of the air currents, we first need to understand the relationship between airspeed, ground speed, and wind speed.

The airspeed of a plane is the speed at which the plane is moving through the air. It is measured relative to the air. The ground speed, on the other hand, is the speed at which the plane is moving over the ground. It is measured relative to the earth.

The difference between the airspeed and the ground speed is caused by the wind. If the plane is flying with a tailwind (wind blowing in the same direction as the plane's heading), the ground speed will be greater than the airspeed. Conversely, if the plane is flying against a headwind (wind blowing in the opposite direction as the plane's heading), the ground speed will be less than the airspeed.

In this problem, we are given the airspeed and the ground speed of the plane. To find the speed and direction of the air currents, we can use the following equation:

Ground speed = Airspeed + Wind speed

In this equation, the wind speed is the difference between the ground speed and the airspeed. The direction of the air currents can be found using the following equation:

Wind direction = True course - Heading

Let's plug in the given values to solve the problem:

Airspeed = 190 miles per hour
Ground speed = 214 miles per hour
Heading = 24.0°
True course = 40.0°

First, we find the wind speed:

Wind speed = Ground speed - Airspeed
Wind speed = 214 mph - 190 mph
Wind speed = 24 mph

Next, we find the wind direction:

Wind direction = True course - Heading
Wind direction = 40.0° - 24.0°
Wind direction = 16.0°

Therefore, the speed of the air currents is 24.0 mph, and the direction of the air currents is 16.0°.