The pole in a lake

1. Jan 10, 2007

powergirl

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'?

2. Jan 10, 2007

Hootenanny

Staff Emeritus
72ft

(damn this 10 character minimum limit)

3. Jan 10, 2007

neutrino

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

4. Jan 10, 2007

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.

5. Jan 10, 2007

dontdisturbmycircles

True, these questions from a jr.high quiz aren't really brain teasers powergirl....

6. Jan 10, 2007

ooo...sorry