SOLUTION: a plane flew720 mi in 3 hr with the wind. it would take 4 hr to travel the same distance against the wind. what is the rate of the plane in still air and the rate of wind?

Let "u" be the speed of the plane at no wind, 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  = 240 mph flying  with    the wind,
and       effective speed is  = 180 mph flying  against the wind.

It gives you two equations 

u + v = 240,    (1)
u - v = 180.    (2)


To solve the system, add the two equations (both sides). You will get

2u = 240 + 180 = 420.   Hence,  u =  = 210.

Thus the speed of the plane at no wind is 210 miles per hour.

Next, from the equation (1) v = 240 - u = 240 - 210 = 30 miles per hour.

Thus the speed of the wind  is 30 miles per hour.

Answer.  The speed of the plane at no wind is 210 miles per hour.

         The speed of the wind  is 30 miles per hour.

Check.  The speed of the plane with the wind is 210 + 30 = 240 mph, and the flight time is  = 3 hours.

        The speed of the plane against the wind is 210 - 30 = 180 mph, and the flight time is  = 4 hours.

        Checks !