Airspeed Math Problem! Help Please

An airplane flying into a headwind travels 348 miles in 2 hours and 54 minutes. On the return flight, the distance is traveled in 2 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

This question is beyond me, I've never done airspeed? Can someone complete the problem step by step so I will know how to do the rest of them I have? Thank you very very much.

Airspeed is the speed of the aircraft relative to the air. Ground speed is the speed of the aircraft relative to the ground, and is the one used to compute the time and distance parameters.

Assuming a direct headwind and tailwind, Ground Speed = Air Speed + Tailwind speed = Airspeed - Headwind Speed.

In the first half of the flight in the problem, the airplane makes good a ground speed of 348/(2+54/60) = 120 miles per hour. On the return flight, the airplane makes good a ground speed of 348/2 = 174 miles per hour.

Since the airplane had a headwind going and a tailwind returning, with A = the airspeed and W the wind speed:

A-W = 120
A+W = 174

Using the techniques of elimination and adding the two equations:
2A = 294
A = 147 mph
W = 174-147 = 27 mph

The airspeed = 147 mph
The wind speed = 27 mph

It works the same way as a boat on a river. The airspeed is the speed of the airplane with respect to the body of air, just as the boats through the water speed is with respect to the water.

For this type of problem you will write two equations in two variables, and then solve by substitution

a = airspeed (mph)
w = windspeed (mph)

2:54 = 2.9 hrs

348 = 2.9(a-w) and 348 = 2.0(a+w)

348/2.9 + w = a and 348/2 - a = w

so

348/2 - 348/2.9 -w = w

(348/2 -348/2.9)/2 = w

27 = w ( wind speed is 27 mph)
348/2 - a = 27
174 - 27 = a

147 = a (airspeed is 147 mph)