1. **State the problem:** We want to find the time $t$ when Spider-Man reaches his maximum swinging distance and the value of that maximum distance. 2. **Given function:** The distance function is $$d(t) = -16t^2 + 32t$$ where $d$ is distance in feet and $t$ is time in seconds. 3. **Formula for vertex of a parabola:** For a quadratic function $ax^2 + bx + c$, the vertex (maximum or minimum) occurs at $$t = -\frac{b}{2a}$$ 4. **Identify coefficients:** Here, $a = -16$ and $b = 32$. 5. **Calculate time of maximum distance:** $$t = -\frac{32}{2 \times -16} = -\frac{32}{-32} = 1$$ seconds. 6. **Calculate maximum distance by substituting $t=1$ into $d(t)$:** $$d(1) = -16(1)^2 + 32(1) = -16 + 32 = 16$$ feet. 7. **Interpretation:** Spider-Man reaches his maximum swinging distance of 16 feet at 1 second. This completes the solution.