Question

A plane is flying through the sky through windy weather. The plane goes 148 miles against the wind in the

same amount of time as it take it to go 248 miles with the wind. If the wind speed is 25 miles per hour,
what is the air speed of the plane?

Answer 1

The airspeed of the plane is found by using the equation that sets the time against the wind equal to the time with the wind. Solving the resulting equation yields an airspeed of 99 miles per hour.

Step-by-step explanation:

To find the airspeed of the plane, we will use the information that the time taken to fly against the wind equals the time taken to fly with the wind. Let's denote the airspeed of the plane as x, which is the speed of the plane in still air. The speed of the wind is given as 25 miles per hour.

When flying against the wind, the effective speed of the plane is x - 25 mph, and it travels 148 miles. When flying with the wind, the effective speed is x + 25 mph, and it travels 248 miles. The times for both journeys are the same, so we can set up the following equation:

Time against the wind = Time with the wind

\(\frac{148}{x - 25} = \frac{248}{x + 25}\)

Cross-multiply to solve for x:

148(x + 25) = 248(x - 25)

Expand and rearrange the equation:

148x + 3700 = 248x - 6200

Subtract 148x from both sides to get:

100x = 9900

Divide both sides by 100 to find x:

x = 99

Therefore, the airspeed of the plane is 99 mph.