# The pole in a lake

powergirl

## Main Question or Discussion Point

The pole in a lake!!

There is a pole in a lake. One-half of the pole is in the ground, another one-third of it is covered by water, and 12 ft is out of the water. What is the total length of the pole in 'ft'?

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Hootenanny
Staff Emeritus
Gold Member
72ft

(damn this 10 character minimum limit)

How is that this is posted under the Brain Teasers section?

powergirl
72ft is correct
Solution:

Fraction of pole in the ground = 1/2
Fraction of pole covered by water = 1/3
Fraction of pole in the ground and covered by water = 1/2 + 1/3 = (3 + 2)/6 = 5/6
Fraction of pole out of water = 1 - 5/6 = 1/6
Thus, one-sixth of the pole (out of water) is 12 ft.
So, total length of pole = 72 ft.

It may be noted that:
Length of pole in the ground = 72/2 = 36 ft.
Length of pole covered by water = 72/3 = 24 ft.
Length of pole out of water = 12 ft.

The problem may also be solved by setting up the following equation: x/2 + x/3 + 12 = x
where x denotes the total length of the pole in ft.
The equation may be solved as shown below.
5x/6 + 12 = x
12 = x - 5x/6 = x/6
x/6 = 12 or x = 72.

How is that this is posted under the Brain Teasers section?
True, these questions from a jr.high quiz aren't really brain teasers powergirl....

powergirl
ooo...sorry