The problem asks: A pole is buried in the ground by one-third of its length. Half of its length is in the water, and 2 meters protrude from the water. What is the length of the pole?

1. Problem Description

The problem asks: A pole is buried in the ground by one-third of its length. Half of its length is in the water, and 2 meters protrude from the water. What is the length of the pole?

2. Solution Steps

Let $x$ be the total length of the pole.

The length of the pole buried in the ground is $\frac{1}{3}x$.

The length of the pole in the water is $\frac{1}{2}x$.

The length of the pole protruding from the water is 2 meters.

The sum of the lengths of these three parts is equal to the total length of the pole.

Thus, we have the equation:

$\frac{1}{3}x + \frac{1}{2}x + 2 = x$

To solve for $x$, we first find a common denominator for the fractions, which is

6. $\frac{2}{6}x + \frac{3}{6}x + 2 = x$

$\frac{5}{6}x + 2 = x$

Subtract $\frac{5}{6}x$ from both sides:

$2 = x - \frac{5}{6}x$

$2 = \frac{6}{6}x - \frac{5}{6}x$

$2 = \frac{1}{6}x$

Multiply both sides by 6:

$2 \cdot 6 = x$

$12 = x$

3. Final Answer

The length of the pole is 12 meters.