A diver is working 10 feet below the surface of the water. The gap between the water and the deck of his support barge is 1/8 of the total length of air hose, and 2/3 of the total length remains on the reel. What is his maximum working depth without a change of equipment?
To find the diver's maximum working depth without a change of equipment, we need to determine the length of the air hose.
Let's assume the total length of the air hose is represented by "x".
According to the problem, the gap between the water and the deck of the support barge is 1/8 of the total length of the air hose. So, the length of this gap would be (1/8) * x.
The length of the air hose remaining on the reel is given as 2/3 of the total length. So, the length remaining on the reel is (2/3) * x.
Now, let's calculate the usable length of the air hose by subtracting the above two lengths:
Usable length = Total length - Length of gap - Length remaining on reel
= x - (1/8) * x - (2/3) * x
= x - (1/8 + 2/3) * x
= x - (27/24) * x
= (24/24) * x - (27/24) * x
= (24 - 27)/24 * x
= -3/24 * x
= -1/8 * x
Since we cannot have a negative length, the usable length cannot be negative. Therefore, -1/8 * x must be greater than or equal to zero.
-1/8 * x ≥ 0
To find the maximum depth, we can equate -1/8 * x to zero:
-1/8 * x = 0
We can solve this equation to find the value of "x" which represents the total length of the air hose.
-1/8 * x = 0
x = 0 / (-1/8)
x = 0
Since x = 0, it means the length of the air hose is zero, which is not possible.
Therefore, there is no usable length of the air hose, and the diver cannot work at any depth without a change of equipment.
1/8 L + 10feet=1/3 L
solve for L.
Then working depth is 10 feet less.