Estimate the number of days it would take to walk around the earth, assuming 12 h walking per day at$4{\mathrm{kmh}}^{-1}$.

The speed of walking,$v=4{\mathrm{kmh}}^{-1}$ .

Assume that the time taken to take a walk around the earth is t, and the radius of the earth is 6,371 km. You can consider the earth a sphere, and thus, the path of walking can be approximated as a circle.

As the path can be approximated as a circle, the length of the path can be written, using the formula of the circumference of a circle, as

$L=2\pi r_{\mathrm{E}}$.

Here, $r_{\mathrm{E}}$is the radius of the earth.

Substituting the value of the radius of the earth in the above equation,

$\begin{array}{c}L=2\pi \times 6371\\ =40,030.17\mathrm{km}\end{array}$

As speed is the distance covered per unit time, the time taken in covering L distance with v speed can be written as

$\begin{array}{c}t=\frac{L}{v}\\ =\frac{40,030.17}{4}\\ =10,007.54\mathrm{h}\end{array}$

Thus, the total time taken in walking around the earth is 10,007.54 h.

As mentioned in the question, a total of 12 h of walking will be done each day. Thus, the total number of days is

$\begin{array}{c}t=\frac{10,007.54}{12}\\ =833.96\\ \approx 834\mathrm{days}\end{array}$

Thus, approximately, it will take 834 days to complete a walk around the earth.