### Brain Teasers

# A 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 9 ft is out of the water. What is the total length of the pole in ft?

### Answer

Fraction of pole in the ground = 1/2Fraction 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 9 ft.

So, total length of pole = 54 ft.

It may be noted that:

Length of pole in the ground = 54/2 = 27 ft.

Length of pole covered by water = 54/3 = 18 ft.

Length of pole out of water = 9 ft.

The problem may also be solved by setting up the following equation: x/2 + x/3 + 9 = x

where x denotes the total length of the pole in ft.

The equation may be solved as shown below.

5x/6 + 9 = x

9 = x - 5x/6 = x/6

x/6 = 9 or x = 54.

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