When three pipes fill a pool, they can finish in 12 hours. Two of the pipes can finish in 18 hours if they are working together. How long would it take a third pipe to fill the pool on its own?
1/T + 1/T + 1/T = 1/12.
3/T = 1/12,
T/3 = 12,
T = 36 hours for 1 pipe.
To solve this problem, we can set up a system of equations based on the information given.
Let's denote the time it takes for the first pipe to fill the pool alone as "x" hours.
We are told that when three pipes are working together, they can fill the pool in 12 hours. This means that the combined rate at which the three pipes fill the pool is 1/12 of the pool per hour.
Similarly, when two pipes are working together, they can fill the pool in 18 hours. Therefore, the combined rate at which the two pipes fill the pool is 1/18 of the pool per hour.
Now, let's translate this information into equations:
Equation 1: (First pipe's rate + Second pipe's rate + Third pipe's rate) = 1/12
Equation 2: (First pipe's rate + Second pipe's rate) = 1/18
From Equation 1, we can say that the combined rate of the first pipe and the second pipe is (1/12 - Third pipe's rate).
Substituting this into Equation 2, we get:
(1/12 - Third pipe's rate) = 1/18
Now, we can solve for Third pipe's rate:
1/12 - Third pipe's rate = 1/18
1/18 = 1/12 - Third pipe's rate
1/18 - 1/12 = - Third pipe's rate
(12 - 18)/(12*18) = - Third pipe's rate
-1/72 = - Third pipe's rate
Therefore, the rate of the third pipe is 1/72 of the pool per hour.
Since we want to find the time it takes for the third pipe to fill the pool alone, we need to find the reciprocal of the rate. Thus, the third pipe alone would take 72 hours to fill the pool.
So, the answer to the question is that it would take the third pipe 72 hours to fill the pool on its own.