Solving a Math Puzzle using Physics

The following math problem, which appeared on a Scottish maths paper, has been making the internet rounds.

The first two parts require students to interpret the meaning of the components of the formula $T(x) = 5 \sqrt{36+x^2} + 4(20-x)$, and the final "challenge" component involves finding the minimum of $T(x)$ over $0 \leq x \leq 20$. Usually this would require a differentiation, but if you know Snell's law you can write down the solution almost immediately. People normally think of Snell's law in the context of light and optics, but it's really a statement about least time across media permitting different velocities.

One way to phrase Snell's law is that least travel time is achieved when $$\frac{\sin{\theta_1}}{\sin{\theta_2}} = \frac{v_1}{v_2},$$ where $\theta_1, \theta_2$ are the angles to the normal and $v_1, v_2$ are the travel velocities in the two media.

In our puzzle the crocodile has an implied travel velocity of 1/5 in the water and 1/4 on land. Furthermore, the crocodile travels along the riverbank once it hits land, so $\theta_2 = 90^{\circ}$ and $\sin{\theta_2} = 1$. Snell's law now says that the path of least time satisfies $$\sin{\theta_1} = \frac{x}{\sqrt{36+x^2}} = \frac{4}{5},$$ giving us $25x^2 = 16x^2 + 24^2$. Solving, $3^2 x^2 = 24^2, x^2 = 8^2$ and the solution is $x = 8$.