SOLUTION: Flying against the wind, an airplane travels 5390 kilometers in 7 hours. Flying with the wind, the same plane travels 3750 kilometers in 3 hours. What is the rate of the plane in s

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


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


From the condition, we have this system of equstions


    u + v = 3750/3 = 1250  mph    (1)

    u - v = 5390/7 =  770  mph    (2)


To solve equations, add them. You will get


    2u = 1250 + 770 = 2020;  hence  u = 2020/2 = 1010  mph.


Then from equation (1),

    v = 1250 - u = 1250 - 1010 = 240 mph.


ANSWER.  The rate of the airplane in still air is 1010 miles per hour;  the rate of the wind is 240 mph.

Post-solution note