Math Word Problem..digging a hole?

Question

Professor Haigh watched a man digging a hole outside the Mathmatics Hall at Northern State University. "how much deeper are you going?" he asked. Knowing where he was working, the digger replied, "I am one third done; and when I am finished the top of my head will be twicea s far below grounda s it nw is above ground." The professor said, "i'll need to know your height if I'm to figure the answer to my question." The man then said that he was five feet, ten inches tall. How deep will the hole be when it is finished?

Answer 1

The digger's height is 70 inches.

Let x be the full depth of the hole when finished (in inches)

So currently the depth is 1/3x. Subtract from 70 and you get the height of his head above the ground.
above = 70 - (1/3)x

Later the hole will be x. Subtract his height (70) and you'll get the distance from the top of his head below ground.
below = x - 70

The ratio between these distances is 2 (below = 2 * above)

x - 70 = 2(70 - 1/3x)
x -70 = 140 - (2/3)x

x + (2/3)x = 210
(5/3)x = 210
x = 210 * 3/5
x = 42 * 3
x = 126

Convert this to inches and you have:
x = 10*12 + 6

So in the end the hole will be 10' 6" feet deep (or 10½ feet).

As a double-check, when he dug 1/3 of the hole, it was 3½ feet (42 inches) deep. Thus his head was 28 inches above the ground.

And when the hole was done, his head was 10' 6" - 5' 10" = 4' 8" = 56 inches below the ground.

56 = 2 * 28, so the answer is correct.

The hole will be 10' 6" deep.

Answer 2

The digger are, 5feet,ten inches = 70 inches.
when his feet are in the bottom, will be 210 inches = 17 feet, 6 inches.

answer = 210 feet