Question

A plane can fly 960 miles with the wind in 3 hours. It takes the same amount of time to fly 840 miles against the wind. What is the speed of the plane in still air and the speed of the wind?

Answer 1

The speed of the plane in still air is 300 miles per hour, and the speed of the wind is 20 miles per hour.

Step-by-step explanation:

To find the speed of the plane in still air and the speed of the wind, we can use the concept of relative velocity. Let's assume the speed of the plane in still air is 'p' and the speed of the wind is 'w'.

When the plane is flying with the wind, its effective speed is the sum of its speed in still air and the speed of the wind: p + w. We can use the formula: Speed = Distance / Time. So, we have 960 miles = (p + w) * 3 hours.

Similarly, when the plane is flying against the wind, its effective speed is the difference between its speed in still air and the speed of the wind: p - w. We have 840 miles = (p - w) * 3 hours.

We can solve these two equations to find the values of 'p' and 'w'.

Let's solve the first equation: 960 miles = (p + w) * 3 hours. Rearranging the equation, we get: 320 = p + w.

Now, let's solve the second equation: 840 miles = (p - w) * 3 hours. Rearranging the equation, we get: 280 = p - w.

By solving these two equations, we can find that the speed of the plane in still air is 300 miles per hour, and the speed of the wind is 20 miles per hour.