Answer:
The width and the length of the pool are 12 ft and 24 ft respectively. 
Step-by-step explanation:
The length (L) of the rectangular swimming pool is twice its wide (W):

Also, the area of the walkway of 2 feet wide is 448:

 
 
Where 1 is for the swimming pool (lower rectangle) and 2 is for the walkway more the pool (bigger rectangle). 
The total area is related to the pool area and the walkway area as follows:
 (1)
    (1)          
The area of the pool is given by:
 
         
 (2)
  (2)          
And the area of the walkway is:
 (3)
    (3)          
Where the length of the bigger rectangle is related to the lower rectangle as follows:                   
 (4)
   (4)        
By entering equations (4), (3), and (2) into equation (1) we have:
 
 
 
                
 
             


By solving the above quadratic equation we have:
W₁ = 12 ft 
Hence, the width of the pool is 12 feet, and the length is:

Therefore, the width and the length of the pool are 12 ft and 24 ft respectively. 
I hope it helps you!