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?
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
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.
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
To determine the depth of the hole, we need to break down the information given and solve for the unknown depth.
Let's assume that the current height of the man's head above the ground is represented by "x" cm. According to the problem, when the man finishes digging the hole, the top of his head will be three times as far under the ground as it is above the ground now.
Based on this information, we can create an equation:
x + 3x = 182
To solve for x, we combine like terms:
4x = 182
Next, we isolate x by dividing both sides of the equation by 4:
x = 182/4 = 45.5
Therefore, the current height of the man's head above the ground is 45.5 cm.
Now, since the problem states that the man has finished one-quarter of the hole, we can determine the depth of the hole. Since the height of his head above the ground is 45.5 cm, one-quarter of that would be:
45.5 / 4 = 11.375 cm
Thus, the depth of the hole is going to be 11.375 cm.