Two pools are being filled with water. To start, the first pool contains 

680

 liters of water and the second pool is empty. Water is being added to the first pool at a rate of 

19,5

 liters per minute. Water is being added to the second pool at a rate of 

40,75

 liters per minute.


After how many minutes will the two pools have the same amount of water?

How much water will be in each pool when they have the same amount?


Let's define the number of minutes after which the two pools will have the same amount of water as \( t \).

### Pool 1:
- Initial amount of water: 680 liters
- Rate of water being added: 19.5 liters per minute

The amount of water in Pool 1 after \( t \) minutes can be expressed as:
\[
\text{Water in Pool 1} = 680 + 19.5t
\]

### Pool 2:
- Initial amount of water: 0 liters (empty)
- Rate of water being added: 40.75 liters per minute

The amount of water in Pool 2 after \( t \) minutes can be expressed as:
\[
\text{Water in Pool 2} = 40.75t
\]

### Finding the time when both pools have the same amount of water:
To find the time \( t \) when the amount of water in both pools is equal, set the two expressions equal to each other and solve for \( t \):

\[
680 + 19.5t = 40.75t
\]

Subtract \( 19.5t \) from both sides:
\[
680 = 21.25t
\]

Solve for \( t \) by dividing both sides by 21.25:
\[
t = \frac{680}{21.25} \approx 32 \text{ minutes}
\]

So, after approximately **32 minutes**, the two pools will have the same amount of water.

### Amount of water in each pool when they are equal:
To find the amount of water in each pool at this time, substitute \( t = 32 \) into either water amount equation.

Using Pool 2's equation (since it's simpler):
\[
\text{Water in Pool 2} = 40.75 \times 32 = 1304 \text{ liters}
\]

Therefore, both pools will have **1304 liters** of water when they have the same amount.

---

Would you like more details on this solution or have any other questions? Here are some related questions to explore:

1. What if the initial amount of water in Pool 1 was different?
2. How long would it take for Pool 2 to completely fill up?
3. How does the rate difference affect the time to equalize the water levels?
4. What if a third pool was also being filled at a different rate?
5. How much water would each pool have after 60 minutes?
6. What if Pool 1's filling rate was increased?
7. How would the situation change if Pool 2 started with some water?
8. What happens if both rates are the same?

**Tip:** When dealing with problems involving rates, setting up equations based on the relationship between time, rate, and quantity can make it easier to find the solution.

Explore how to determine when two pools, one starting with 680 liters and the other empty, will have equal amounts of water. Learn the step-by-step solution involving rates of water addition and initial quantities. Suitable for students in Grades 6-8.

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