SOLUTION: A jet plane flying with the wind went 1780 mi in 4 h. Against the wind, the plane could only fly 1520 mi in the same amount of time. Find the rate of the plane in calm air and th

Let "u" be the speed of the plane at no wind (=same as in calm air), in mph.
Let "v" be the speed of wind.

Then the effective speed of the plane flying WITH the wind is (u+v) mph (relative to the ground).

the effective speed of the plane flying AGAINST the wind is (u-v) mph (relative to the ground).

According to the condition, 
the plane effective speed is  = 445 mph flying  with    the wind,
and       effective speed is  = 380 mph flying  against the wind.

It gives you two equations 

u + v = 445,    (1)
u - v = 380.    (2)

Add the two equations (both sides). You will get

2u = 445 + 380 = 825.   Hence,  u =  = 412.5.

Thus the speed of the plane at no wind is 412.5 mph.

Next, from the equation (1) v = 445 - u = 445 - 412.5 = 32.5 mph.

Thus the speed of the wind  is 32.5 mph.

Answer.  The speed of the plane at no wind is 412.5 mph.

         The speed of the wind  is 32.5 mph.

Check.  The speed of the plane with the wind is 412.5 + 32.5 = 445 mph, and the flight time is  = 4 hours.

        The speed of the plane against the wind is 412.5 - 32.5 = 380 mph, and the flight time is  = 4 hours.

        Checks !