1. Let's first understand the problem: We want to find how fast it would take to cover the distance of the whole circumference of the universe, which is not fixed and is changing over time. 2. The circumference of a universe modeled as a sphere is given by the formula $$C = 2\pi R$$ where $R$ is the radius of the universe. 3. Since the radius $R$ is changing over time, we denote it as $R(t)$, and the circumference also changes as $$C(t) = 2\pi R(t)$$. 4. To find how fast the circumference changes, we differentiate $C(t)$ with respect to time $t$: $$\frac{dC}{dt} = 2\pi \frac{dR}{dt}$$ 5. Here, $\frac{dR}{dt}$ is the rate of change of the radius of the universe, which depends on cosmological models and observations (like the Hubble constant). 6. If you want to find the time $T$ to cover the circumference at a speed $v$, then: $$T = \frac{C(t)}{v} = \frac{2\pi R(t)}{v}$$ 7. Since $R(t)$ is changing, the time $T$ also changes over time. 8. Without specific values for $R(t)$ and $v$, we cannot compute a numerical answer, but the key takeaway is that the speed to cover the circumference depends on the instantaneous radius and the speed chosen. 9. In summary, the problem involves understanding the dynamic circumference $$C(t) = 2\pi R(t)$$ and the time to cover it $$T = \frac{2\pi R(t)}{v}$$ where $v$ is the travel speed.