Math / Algebra

QuestionTwo pools are being filled with water. To start, the first pool contains 784 liters of water and the second pool is empty. Water is being added to the first pool at a rate of 18.25 liters per minute. Water is being added to the second pool at a rate of 42.75 liters per minute.
After how many minutes will the two pools have the same amount of water? $\square$ minutes
How much water will be in each pool when they have the same amount? $\square$ titers

Studdy Solution

STEP 1

1. The first pool starts with 784 liters of water.
2. The second pool starts with 0 liters of water.
3. Water is added to the first pool at a rate of 18.25 liters per minute.
4. Water is added to the second pool at a rate of 42.75 liters per minute.
5. We need to find the time in minutes when both pools have the same amount of water.
6. We need to find the amount of water in each pool when they have the same amount.

STEP 2

1. Define variables for the problem.
2. Write equations for the amount of water in each pool over time.
3. Set the equations equal to each other to find the time when the pools have the same amount of water.
4. Solve the equation for time.
5. Calculate the amount of water in each pool at that time.

STEP 3

Define variables for the problem.
Let $t$ be the time in minutes after which both pools have the same amount of water.

STEP 4

Write equations for the amount of water in each pool over time.
For the first pool, the amount of water $W_1(t)$ is given by: $W_1(t) = 784 + 18.25t$
For the second pool, the amount of water $W_2(t)$ is given by: $W_2(t) = 42.75t$

STEP 5

Set the equations equal to each other to find the time when the pools have the same amount of water.
$784 + 18.25t = 42.75t$

STEP 6

Solve the equation for time.
Subtract $18.25t$ from both sides: $784 = 42.75t - 18.25t$
Simplify the right side: $784 = 24.5t$
Divide both sides by 24.5 to solve for $t$ : $t = \frac{784}{24.5}$
Calculate $t$ : $t = 32$

STEP 7

Calculate the amount of water in each pool at that time.
Substitute $t = 32$ back into either equation for the amount of water:
Using the first pool's equation: $W_1(32) = 784 + 18.25 \times 32$
Calculate: $W_1(32) = 784 + 584 = 1368$
Thus, when the pools have the same amount of water, each pool contains: $\boxed{1368}$ liters

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Studdy Solution

STEP 1

STEP 2

1. Define variables for the problem.
2. Write equations for the amount of water in each pool over time.
3. Set the equations equal to each other to find the time when the pools have the same amount of water.
4. Solve the equation for time.
5. Calculate the amount of water in each pool at that time.

STEP 3

Define variables for the problem.
Let $t$ be the time in minutes after which both pools have the same amount of water.

STEP 4

Write equations for the amount of water in each pool over time.
For the first pool, the amount of water $W_1(t)$ is given by: $W_1(t) = 784 + 18.25t$
For the second pool, the amount of water $W_2(t)$ is given by: $W_2(t) = 42.75t$

STEP 5

Set the equations equal to each other to find the time when the pools have the same amount of water.
$784 + 18.25t = 42.75t$

STEP 6

Solve the equation for time.
Subtract $18.25t$ from both sides: $784 = 42.75t - 18.25t$
Simplify the right side: $784 = 24.5t$
Divide both sides by 24.5 to solve for $t$ : $t = \frac{784}{24.5}$
Calculate $t$ : $t = 32$

STEP 7

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Studdy Solution

STEP 1

STEP 2

1. Define variables for the problem.2. Write equations for the amount of water in each pool over time.3. Set the equations equal to each other to find the time when the pools have the same amount of water.4. Solve the equation for time.5. Calculate the amount of water in each pool at that time.

STEP 3

Define variables for the problem.Let t t t be the time in minutes after which both pools have the same amount of water.

STEP 4

STEP 5

Set the equations equal to each other to find the time when the pools have the same amount of water.784+18.25t=42.75t 784 + 18.25t = 42.75t 784+18.25t=42.75t

STEP 6

STEP 7

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Define variables for the problem.
2. Write equations for the amount of water in each pool over time.
3. Set the equations equal to each other to find the time when the pools have the same amount of water.
4. Solve the equation for time.
5. Calculate the amount of water in each pool at that time.

Define variables for the problem.
Let $t$ be the time in minutes after which both pools have the same amount of water.

Set the equations equal to each other to find the time when the pools have the same amount of water.
$784 + 18.25t = 42.75t$