### 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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## Comments

Again, these are supposed to be "teasers", not 6th grade arithmetic.

Well, if you do not like math, then why ar you looking at teasers in the math section? Also, I am in 6th grade and thank-you-very-much we have not learned that yet. My sister gave it to me. We learn algebra in 7th grade. Right now we're only learning pre-algebra.

I thought it was good, it was kinda fun and took half a minute, which is normal.

I am one of those who complains about problems fobbed off as teasers. Until there is a category or some symbol to designate them as juvenile exercises, I claim the right to be annoyed. A teaser should, by definition, "require a lot of thought." A lot of calculating is not the same thing.

Easy but at least the author went to some trouble to explain the solution which is more than be said for many other teasers.

I am in 7th grade, and we learned what was needed to solve this a looooong time ago. No algebra needed - 1/2 plus1/3 is 5/6. So 9 is 1/6 of it, 9x6=54. I did it in my head in like half a minute!

This teaser does not require a lot of thought OR a lot of calculating.

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