we will assume that the return trip with the wind took 2 2/3 = 8/3 hours

Let

p = plane speed in still air

w = wind speed

t1 = 3 hr the time of the trip against the wind

d = 1,440 mi the distance in one direction

t2 = 8/3 hr the time of the return trip with the wind

traveling with against the wind the speed of the plane is p - w

p - w = d/t1

p - w = 1440/3

p - w = 480

traveling with the wind the speed of the plane is p + w

p + w = d/t2

p + w = 1440/(8/3)

p + w = 540

by solving the system of equations

p - w = 480

p + w = 540

we find

p = 510 mph

w = 30 mph

click here to see the step by step solution of the system of equations

The speed of the plane is 510 mph.

The wind-speed is 30 mph.