SOLUTION: Flying against a jet stream, a jet travels 4500 miles in 9 hours. Flying with jet stream, the same jet travels 3760 in 4 hours. What is the rate of the jet in still air and what is

    Jet streams are some of the strongest winds in the atmosphere. 
    Their speeds usually range from 129 to 225 kilometers per hour (80 to 140 miles per hour), 
    but they can reach more than 443 kilometers per hour (275 miles per hour).

    https://www.nationalgeographic.org/encyclopedia/jet-stream/#:~:text=Jet%20streams%20are%20some%20of,(275%20miles%20per%20hour).

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


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


From the condition, we have this system of equations


    u + v = 3760/4 = 940  mph    (1)

    u - v = 4500/9 = 500  mph    (2)


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


    2u = 940 + 500 = 1440;  hence  u = 1440/2 = 720  mph.


Then from equation (1),

    v = 940 - u = 940 - 720 = 220 mph.


ANSWER.  The rate of the airplane in still air is 720 miles per hour;  
         the rate of the jet stream is 220 miles per hour.