Answer:
Width = 6ft Area = 54 sq ft
Step-by-step explanation:
First, re-read the problem until you understand it and can put it into your own words.  I re-wrote it like this:  "Find the area of a rectangle by first finding the length (L) and the width (W)."   [note that I added "find L and W," but that is how I'm going to solve the problem;  I could also have said that we will need the formulas, P=2L+2W and A=LW, but you knew that already, right?).
  
Translate the problem:
  "The length of a rectangle is 3 ft longer than its width"      means
          L                             =    3             +         W                 (eq1)
  "the perimeter of the rectangle is 30 ft"     means
             P                                = 30                      (eq2)
  
So, now the math is easy, just find L and W so we can compute the area:
      P = 30 = 2L + 2W                         (eq3; from eq2 and the formula for P)
           30 = 2(3+W)  +  2W              (use eq1 to substitute for L)
           30 = 6 + 2W   + 2W              (distribute)
            30 = 6 + 4W                       (collect terms)
             24 = 4W                        (subtract 6 from both sides)
             6 ft = W                         (divide both sides by 4)
  
Use the easiest equation (either eq1 or else eq3) to find L:
           L = 3 + W        (eq1)
           L = 3 + 6
           L = 9 ft
What is the area (A)?
           A = L*W
           A = (9 ft)*(6 ft)
           A = 54 sq ft