If two inlet pipes are open, they can fill a pool in 1 & 12 minutes, one of the pipes can fill the pool itself in 2 hours. How long will it take the other pipe to fill the pool by itself?

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To solve this problem, we can assign variables to the unknowns and use algebraic equations to solve for the desired value.

Let's denote the time it takes for the first pipe to fill the pool alone as "t" (in minutes).

Given that two inlet pipes can fill the pool in 1 & 12 minutes, we can determine their relative rates. The rate of filling for the two pipes together is the sum of their individual rates.

Since one pipe can fill the pool alone in 2 hours (120 minutes), its rate of filling would be 1 pool per 120 minutes, which is 1/120 pools per minute.

From here, we can set up the equation:
1/1 + 1/12 = 1/t

Simplifying this equation, we get:
12/12 + 1/12 = 1/t
13/12 = 1/t

To solve for "t," we can rearrange the equation:
12/t = 13/1

Cross-multiplying, we have:
12 = 13t

Dividing both sides by 13, we find:
12/13 = t

Therefore, it will take the other pipe 12/13 minutes to fill the pool alone.

Note: We converted the 2 hours given for the first pipe to minutes for consistency in units throughout the problem.