SOLUTION: An airplane travels 5096 kilometers against the wind in 7 hours and 5796 kilometers with the wind in the same amount of time. What is the rate of the plane still air and what is th

Let u be the airplane rate in still air (in kilometers per hour), and
let v be the rate of wind.


Then the airplane's effective speed flying with the wind is u+v kilometers per hour,
while its effective speed flying against the wind is u-v kilometers per hour.


From the condition, we have this system of equations


    u + v = 5796/7 = 828  km/h    (1)

    u - v = 5096/7 = 728  km/h    (2)


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


    2u = 828 + 728 = 1556;  hence  u = 1556/2 = 778  km/h.


Then from equation (1),

    v = 828 - u = 828 - 778 = 50 km/h.


ANSWER.  The rate of the airplane in still air is 778 kilometers per hour;  
         the rate of the wind is 50 kilometers per hour.