They are separating at the rate of 450+550 = 1000 mi/h.

We use the formula  with D = 4000 mi and R = 1000 mi/h
                   
                   
                   

answer: 4 hours.

Edwin

Let t be the time under the question, in hours.

Then the first   plane will cover the distance  450*t miles in t hour,
while the second plane will cover the distance  550*t miles in t hour.


Since they fly in opposite directions, the distance between them in t hours will be 

450*t + 550*t.


According to the condition, the distance is 4000 miles. It gives an equation

450*t + 550*t = 4000.

Simplify and solve for t:

(450+550)*t = 4000 ====>  1000*t = 4000  ====>  t =  = 4 hours.


Answer.  It will take 4 hours.

Since their relative speed is 450 km/h + 550 km/h, the distance between the planes increases at the rate (450 + 550) = 1000 km/h.


Now apply the formula  t =  =  = 4 hours.


You get the same answer.