### Brain Teasers

# Half a Hole

While digging a hole his back he did bend.

When asked how deep it would be in the end,

He replied "I'm halfway, and this I will vow,

You can see how far above the top my head is now".

"But when it is finished, as sure as my name is Ken,"

"My head will be twice as far below the top then."

"Pray tell me dear Kenneth, what is your height?"

"I'm one metre sixty!" Can you get the depth right?

When asked how deep it would be in the end,

He replied "I'm halfway, and this I will vow,

You can see how far above the top my head is now".

"But when it is finished, as sure as my name is Ken,"

"My head will be twice as far below the top then."

"Pray tell me dear Kenneth, what is your height?"

"I'm one metre sixty!" Can you get the depth right?

### Answer

The final depth will be 2.4 metres.Let x = the hole's final depth, and y = the height above ground level that Ken's head is now.

From the first statement you can set up the equation:

x/2 + y = 1.6

(Half the final hole depth + the height Ken's head is above ground level = Ken's height)

From the second statement you can set up the equation:

x - 2y = 1.6

(The final depth of the hole - twice the height that Ken's head is currently above ground level = Ken's height).

Solve these for x to get the answer of 2.4 metres.

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## Comments

Very math-ish, good job!

Good job, 'cept it says that he was bent when he made the comment about how high his head was at the time. If that were the case, it would be impossible to figure the final depth.

I'm not sure why you would set up the equation with two variables.

Where x is the height of the man above the hole when he answers the question, the equation is:

2(1.6 - x) = 1.6 + 2x

3.2 - 2x = 1.6 + 2x

1.6 = 4x

x = .4

Just plug x into either side of the original equation to get the depth of the hole.

Did it in my head in about 15 seconds.

Where x is the height of the man above the hole when he answers the question, the equation is:

2(1.6 - x) = 1.6 + 2x

3.2 - 2x = 1.6 + 2x

1.6 = 4x

x = .4

Just plug x into either side of the original equation to get the depth of the hole.

Did it in my head in about 15 seconds.

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