Two rectangles have the same width. the length of one is 2 feet longer than the width. the length of the other is 4 feet longer than the width. the larger rectangle has 8 more square feet than the smaller. what is the width of the rectangles?

Since both the rectangles have the same width,
Let us assume the width of the two rectangles = w
Then
Length of the smaller rectangle = w + 2
Length of the larger rectangle = w + 4
So
Area of the smaller rectangle = w (w + 2)
                                               = w^2 + 2w
Area of the larger rectangle = w (w + 4)
                                             = w^2 + 4w
Now we already know from the question that the larger rectangle has 8 more squares than the smaller rectangle. Based on this information, we can write
w^2 + 2w + 8 = w^2 + 4w
4w - 2w = 8
2w = 8
w = 8/2
    = 4 feet
So the width of the rectangles is 4,feet as can be seen from the above deduction.