To find the maximum area that the fence can enclose, we can analyze the quadratic equation given:
\[ A = -w^2 + 60w \]
This is in the standard form of a quadratic equation \( A = ax^2 + bx + c \) where \( a = -1 \), \( b = 60 \), and \( c = 0 \).
The maximum value of a quadratic function occurs at the vertex, which for the equation \( w = -\frac{b}{2a} \).
- Calculate \( w \):
\[ w = -\frac{60}{2(-1)} = \frac{60}{2} = 30 \]
- Now, substitute \( w = 30 \) back into the area equation to find the maximum area:
\[ A = -30^2 + 60(30) \] \[ A = -900 + 1800 \] \[ A = 900 \]
Thus, the maximum area that Nora can enclose with the fence is \( \boxed{900} \) square feet.