To solve this problem, let's assume the total length of the pole is represented by the variable $x$.
According to the given information:
- One-half of the pole is in the ground, which means $\frac{1}{2}x$ of the pole is in the ground.
- Another one-third of the pole is covered by water, which means $\frac{1}{3}x$ of the pole is covered by water.
- 11 ft is out of the water, which means $11$ ft of the pole is out of the water.
To find the total length of the pole, we need to add up the lengths of each part:
$\frac{1}{2}x + \frac{1}{3}x + 11 = x$
To solve this equation, we can use the concept of common denominators.
Multiplying each term by the least common multiple of 2 and 3, which is 6, we get:
$3(\frac{1}{2}x) + 2(\frac{1}{3}x) + 66 = 6x$
Simplifying the equation:
$\frac{3}{2}x + \frac{2}{3}x + 66 = 6x$
Combining like terms:
$\frac{9}{6}x + \frac{4}{6}x + 66 = 6x$
$\frac{13}{6}x + 66 = 6x$
Multiplying each term by 6 to eliminate the fraction:
$13x + 396 = 36x$
Rearranging the equation:
$36x - 13x = 396$
$23x = 396$
Dividing both sides by 23:
$x = \frac{396}{23} \approx 17.22$
Therefore, the total length of the pole is approximately 17.22 ft.
Among the given options, B) 66 is the closest option to the actual length of the pole, which is 17.22 ft.