let

v = the speed of the plane in still air

w = the speed of the wind

d = 1200 mi the distance from A to B traveled in each direction

t1 = 5 h the time of the trip with the wind

t2 = 8 h the time of the trip against the wind

since speed = distance/time follows distance = speed*time

traveling with the wind the speed of the plane is: v + w

(v + w)*t1 = d

(v + w)*5 = 1200 divide both sides by 5

v + w = 240

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

(v - w)*t2 = d

(v - w)*8 = 1200 divide both sides by 8

v - w = 150

by solving the system of equations:

v + w = 240

v - w = 150

we find:

v = 195 mph

w = 45 mph

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

the speed of the wind is 45 mph.