Math Problem Statement
Solution
The problem you provided involves three pipes that can fill a pool, each with a constant flow rate. Here's a breakdown of the problem:
Problem Statement (Translated):
We have three pipes with a constant flow rate. When the first and second pipes are used simultaneously, they take the same amount of time to fill the pool as the first pipe alone would take. The second pipe alone fills the pool in 5 hours less than the first, and the third pipe fills the pool in 4 hours more than the first.
The question is: How long does it take for each individual pipe to fill the pool on its own?
Let’s define the time each pipe takes to fill the pool as:
- for the first pipe,
- for the second pipe,
- for the third pipe.
From the problem, we know:
-
The second pipe fills the pool 5 hours faster than the first pipe:
. -
The third pipe fills the pool 4 hours slower than the first pipe:
. -
The combined time of the first and second pipes equals the time of the first pipe alone. The inverse of time represents the flow rate, so the equation for the combined work is:
Substituting into this equation:
Now we can solve this equation for and then find and .
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Math Problem Analysis
Mathematical Concepts
Algebra
Rate Problems
Formulas
1/t1 + 1/t2 = 1/t1 (for the combined flow rate)
t2 = t1 - 5 (relation between the first and second pipe)
t3 = t1 + 4 (relation between the first and third pipe)
Theorems
Inverse rate theorem
Suitable Grade Level
Grade 9-11
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