A 182 cm tall man is digging a hole in the ground. He stops for a moment and says: "I am done with one quarter of the hole. When I finish the job the top of my head is going to be three times as far under the ground as far it is above the ground now." How deep is the hole going to be?

CORRECT answer is needed by April 14th, BY THE LATEST.

d1 = 182cm above gnd.

d2 = 3*182 = 546 cm below gnd.
d3 = 182 cm from head to bottom of hole.

D=d1 + d2 + d3=182 + 546 + 182=910 cm =
Depth of the hole.

Correction:

D = d2 + d3 = 546 + 182 = 728 cm.

To find the depth of the hole, we need to break down the information given. Let's assume that when the man says he is done with one quarter of the hole, he means he has dug one-fourth of the final depth.

Let's represent the total depth of the hole as "D" (in centimeters). According to the statement, when the man has finished digging, the top of his head will be three times as far under the ground as it is now above the ground.

Currently, the top of his head is at a height of 182 cm from the ground. After completing the hole, the top of his head will be three times further below the ground than above it. This means the distance his head will be below the ground is 3 times 182 cm, or 546 cm.

Since he has completed one-fourth of the hole, we can represent this as 1/4D. At the end of the digging, the depth of the hole will be D.

According to the information given, the top of his head will be 546 cm below the ground. So, the equation representing the depth of the hole can be expressed as:

D = (182 cm + 546 cm) + (1/4D)

Now, we can solve this equation to find the value of D, which represents the depth of the hole.

First, add 182 cm and 546 cm:

D = 728 cm + (1/4D)

Next, subtract (1/4D) from both sides to isolate D:

D - (1/4D) = 728 cm

Combine the terms on the left side of the equation:

(3/4D) = 728 cm

To find D, multiply both sides by 4/3:

D = (728 cm) * (4/3)
D = 971.33 cm

Therefore, the depth of the hole will be approximately 971.33 cm.