SOLUTION: Flying with the wind, a plane flew 1200 mi in 5 h. Against the wind, the plane required 6 h to fly the same distance. Find the rate of the plane in calm air and the rate of the win

From the condition, you have these two equations

 = u + v,   (1)   (flying with wind, the equation for the speed)

 = u - v.   (2)   (flying against the wind)

Here u is the plane speed at no wind, v is the wind speed.

Simplify the system (1), (2):

u + v = 240,      (3)
u - v = 200.      (4)

To solve it, add the equations (3) and (4). You will get

2u = 240 + 200  --->  2u = 440  --->  u =  = 220.

You just found the speed of the plane at no wind. It is 220 mph.

Now you can easily find v from (1): v = 240 - u = 240 - 220 - 20.

Thus the speed of the wind is 20 mph.

Answer.  Speed of the plane at no wind is 220 mph.  The speed of the wind is 20 mph.