Answer:Swhen they have the same amount of water, each pool will have 2190 liters of water.
Step-by-step explanation:To find out when the two pools will have the same amount of water, we need to set up an equation where the total amount of water in each pool is equal.
Let's denote:
- \( t \) as the number of minutes passed.
- \( W_1 \) as the amount of water in the first pool after \( t \) minutes.
- \( W_2 \) as the amount of water in the second pool after \( t \) minutes.
Initially, the first pool contains 1300 liters of water, and the second pool contains 970 liters of water.
After \( t \) minutes, the amount of water added to the first pool is \( 22.25 \times t \) liters, and the amount of water added to the second pool is \( 30.5 \times t \) liters.
So, our equation becomes:
\[ 1300 + 22.25t = 970 + 30.5t \]
To solve for \( t \), we'll isolate \( t \) on one side of the equation:
\[ 22.25t - 30.5t = 970 - 1300 \]
\[ -8.25t = -330 \]
Dividing both sides by -8.25:
\[ t = \frac{-330}{-8.25} \]
\[ t = 40 \]
So, after 40 minutes, the two pools will have the same amount of water.
To find out how much water will be in each pool when they have the same amount, we substitute \( t = 40 \) back into one of the equations.
Using \( W_1 \):
\[ W_1 = 1300 + 22.25 \times 40 \]
\[ W_1 = 1300 + 890 \]
\[ W_1 = 2190 \text{ liters} \]
Using \( W_2 \):
\[ W_2 = 970 + 30.5 \times 40 \]
\[ W_2 = 970 + 1220 \]
\[ W_2 = 2190 \text{ liters} \]
So, when they have the same amount of water, each pool will have 2190 liters of water.
Answer:Swhen they have the same amount of water, each pool will have 2190 liters of water.
Step-by-step explanation:To find out when the two pools will have the same amount of water, we need to set up an equation where the total amount of water in each pool is equal.
Let's denote:
- \( t \) as the number of minutes passed.
- \( W_1 \) as the amount of water in the first pool after \( t \) minutes.
- \( W_2 \) as the amount of water in the second pool after \( t \) minutes.
Initially, the first pool contains 1300 liters of water, and the second pool contains 970 liters of water.
After \( t \) minutes, the amount of water added to the first pool is \( 22.25 \times t \) liters, and the amount of water added to the second pool is \( 30.5 \times t \) liters.
So, our equation becomes:
\[ 1300 + 22.25t = 970 + 30.5t \]
To solve for \( t \), we'll isolate \( t \) on one side of the equation:
\[ 22.25t - 30.5t = 970 - 1300 \]
\[ -8.25t = -330 \]
Dividing both sides by -8.25:
\[ t = \frac{-330}{-8.25} \]
\[ t = 40 \]
So, after 40 minutes, the two pools will have the same amount of water.
To find out how much water will be in each pool when they have the same amount, we substitute \( t = 40 \) back into one of the equations.
Using \( W_1 \):
\[ W_1 = 1300 + 22.25 \times 40 \]
\[ W_1 = 1300 + 890 \]
\[ W_1 = 2190 \text{ liters} \]
Using \( W_2 \):
\[ W_2 = 970 + 30.5 \times 40 \]
\[ W_2 = 970 + 1220 \]
\[ W_2 = 2190 \text{ liters} \]
So, when they have the same amount of water, each pool will have 2190 liters of water.
