let

w = the speed of the wind

v = the speed of the plane in still air

d = 1764 mi the distance traveled in each direction

t1 = 3.8 hr

t2 = 3 hr

traveling against the wind the speed of the plane is v - w

since speed = distance/time we have

v - w = d/t1

v - w = 1764/3.8

On the return trip, it travels the same 1764 miles in 3 hours. We will assume that there is no wind on the way back:

v = d/t2

v = 1764/3

plug the value for v into v - w = 1764/3.8

1764/3 - w = 1764/3.8

by solving we find:

w = 123.79 mph

click here to see the step by step solution of the equation:

the speed of the wind is 123.79 mph.