An airplane flying into a headwind travels the 1650-mile flying distance between two cities in 3 hours and 18 minutes.


On the return flight, the distance is traveled in 3 hours.

Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

upwind speed = u -w

downwind speed = u+w

1650 = (u-w)(3.3 hours)
1650 = (u+w)(3)

3 u + 3 w = 1650
3.3 u - 3.3 w = 1650

3.3 u + 3.3 w = 1.1*1650 = 1815
3.3 u - 3.3 w = 1650
-------------------- add
6.6 u = 3465
u = 525 miles/hour
now find w

To find the airspeed of the plane and the speed of the wind, we can use the concept of relative velocity.

Let's assume the airspeed of the plane is "x" miles per hour, and the speed of the wind is "w" miles per hour. When the plane is flying with the headwind, the combined speed of the plane and the wind will be the airspeed minus the wind speed, i.e., (x - w) miles per hour.

Given that the flying distance between the two cities is 1650 miles and the time taken is 3 hours and 18 minutes (or 3.3 hours), we can set up the following equation:

Distance = Speed * Time

1650 = (x - w) * 3.3

Similarly, on the return flight, the combined speed of the plane and the wind will be the airspeed plus the wind speed, i.e., (x + w) miles per hour. The flying distance is still 1650 miles, and the time taken is 3 hours, so we can set up the following equation:

Distance = Speed * Time

1650 = (x + w) * 3

Now we have a system of two equations. We can solve this system to find the values of x (airspeed of the plane) and w (speed of the wind).

Let's start by solving the first equation:

1650 = (x - w) * 3.3

Divide both sides of the equation by 3.3:

1650 / 3.3 = x - w

500 = x - w

Now let's solve the second equation:

1650 = (x + w) * 3

Divide both sides of the equation by 3:

1650 / 3 = x + w

550 = x + w

Now we have a system of two equations:

500 = x - w ---(1)
550 = x + w ---(2)

We can add equations (1) and (2) to eliminate the variable "w":

500 + 550 = (x - w) + (x + w)

1050 = 2x

Divide both sides of the equation by 2:

1050 / 2 = x

525 = x

Now that we have found the value of x (airspeed of the plane), we can substitute it back into one of the equations to find the value of w (speed of the wind). Let's use equation (2):

550 = x + w

550 = 525 + w

Subtract 525 from both sides of the equation:

550 - 525 = w

25 = w

Therefore, the airspeed of the plane is 525 miles per hour, and the speed of the wind is 25 miles per hour.