SOLUTION: Flying with the wind, a plane can travel 1100 miles in 4 hours. Against the wind, the plane requires 5 hours to fly the same distance. Find the speed of the plane in calm air and t

The effective speed with the wind is   = 275 mph,

    and it is equal to the sum of the plane speed at no wind,  "u",  and the speed of the wind,  "v"

        u + v = 275.      (1)



The effective speed against the wind is   = 220 mph,

    and it is equal to the DIFFERENCE of the plane speed at no wind and the speed of the wind

        u - v = 220.      (2)



Thus you have these two equations, (1) and (2) for two unknowns, u and v.


To solve the system, add the equations. You will get then  


        2u = 275 + 220 = 495

         u             = 495/2 = 247.5 miles per hour.


Then from equation (1),

        v = 275 - 247.5 = 27.5 miles per hour.



ANSWER.  The speed of the plane at no wind is  247.5 miles per hour.

         The speed of the wind is  27.5 miles per hour.