A private plane can make a 125-mile trip in half an hour when flying against a certain headwind.

win the same wind, it can make the trip in 25 minutes. Find the speed of the wind and the plane's airspeed.

25 mile/h is the speed of the wind.

275 mile/h is the speed of the airplane

Step-by-step explanation:

In this case, let's do this in parts. In the first part, we are going to get the speed of the airplane when it's against the wind, and with the wind.}

To get speed, you need to use the formula of speed:

V = d/t

Where:

V: Speed

d: distance

t: time

Before we use the formula, let's convert the time units from minutes to hour:

t1 = 30 min * 1 h/60 min = 0.5 h

t2 = 25 * 1h/60 min = 0.4167 h

Now, let's solve for the speed against the wind, and with the wind (V1 and V2):

V1 = 125 mile / 0.5 h = 250 mile/h or 250 mph.

V2 = 125 / 0.4167 = 299.98 mph. Let's round this to 300 mph.

Now to get the speed of the wind, we need to get the difference of these speeds and then divide it by 2, (because there are 2 trips)

V = 300 - 250 / 2 = 50 / 2 = 25 mph is the speed of the wind.

Finally for the speed of the airplane, simply get the difference between the speed of the wind and V2, or the sum of the speed of the wind and V1. This is because in V1, you are against the wind, and that's why the speed is lower. In V2 you are with the wind, so the airplane is faster and we need to get the difference of that speed.

So:

V' = 250 + 25 = 275 mph

V' = 300 - 25 = 275 mph