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?

Answer 1

if the hole's depth is d, then the man's head is (182-d) above ground now.

Assuming that the hole is going to be 4 times as deep as it is now, by that time,

4d-182 = 3(182-d)
d = 104

check:
182-104 = 78
416-182 = 234 = 3*78

Answer 2

Pretty sure the previous answer is incorrect, as the man's head wouldn't be three times as far under the ground as far it is above the ground now.

Answer 3

416 cm hole

say hole depth is x
initially hes at 182+x/4
when hes done the distance between his head and ground level will be 3(182-x/4)assuming hes standing up so the depth of the hole is 182+3(182-x/4)
182+3(182-x/4)=x
182+546-(3x/4)=x
728-(3x/4)=x
2912-3x=4x
2912=7x
x=416

416-182= 234 distance between head and ground level after completion

182-x/4=182-104=78 (initial head distance from the ground)

78*3=234 final head distance from the ground