Pittsburgh to Phoenix Flight Time: 3h 36m - Airspeed & Wind Speed Calculation

[Hollysmoke]

An airplane flying into a headwind travels the 1800 mile flying distance between Pittsburgh, Pennsylvania, and Phoenix, Arizona, in three hours and 36 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.

I tried using vectors but...I'm just lost on this question.

 

[Kazza_765]

Well, if this question is supposed to be as straightforward as it sounds, then I assume they mean the speed of the plane stays constant relative to the wind speed.

Then, on the first flight, the plane travels at a speed of vp - va, and on the return flight it travels at a speed of vp + va, where vp is plane speed and va is air speed.

You should be able to set up simultaneous equations and solve for the two unknowns.

 

[kyle8921]

I understand your confusion with this problem. Let me break it down for you.

First, let's define some variables:
- d: distance between Pittsburgh and Phoenix (1800 miles)
- t1: time for the outbound flight (3 hours and 36 minutes)
- t2: time for the return flight (3 hours)
- v: airspeed of the plane
- w: speed of the wind

Now, we can use the formula:
d = vt

For the outbound flight:
1800 miles = v * (3.6 hours)
v = 500 miles per hour

For the return flight:
1800 miles = v * 3 hours
v = 600 miles per hour

We can set up a system of equations to solve for the variables:

500 = v + w (since the plane is flying into a headwind)
600 = v - w (since the plane is flying with a tailwind)

Solving for v, we get:
v = 550 miles per hour

Substituting back into the first equation, we can solve for w:
500 = 550 + w
w = -50 miles per hour

Therefore, the airspeed of the plane is 550 miles per hour and the speed of the wind is 50 miles per hour.

I hope this helps clarify the problem and the solution for you. Keep in mind that this is assuming that both the airspeed and wind speed remain constant throughout the flight. Realistically, these variables can change and affect the flight time. But for the purposes of this problem, we are assuming constant speeds.