A tank starts off containing 1,375 gallons of water, and 28 gallons of water leaks from the tank every hour. At the same time, an empty pool is filled with water at a rate of 560 gallons per hour.

Which inequality represents all possible values of x, the number of hours that have passed when the tank contains less water than the pool?
A.1,375 + 28x > 560x
B.1,375 – 28x > 560x
C.1,375 – 28x < 560x
D.1,375 + 28x < 560x

We are asked to find when the tank contains **less water** than the pool, represented by an inequality in terms of \( x \), the number of hours that have passed.

### Step 1: Write expressions for the water in the tank and pool.

- **Tank**: The tank starts with 1,375 gallons, and 28 gallons of water leaks out every hour. After \( x \) hours, the amount of water in the tank will be:
  \[
  \text{Water in tank} = 1375 - 28x
  \]
  
- **Pool**: The pool is filled at a rate of 560 gallons per hour, so after \( x \) hours, the amount of water in the pool will be:
  \[
  \text{Water in pool} = 560x
  \]

### Step 2: Set up the inequality

We are asked to find when the tank contains **less water** than the pool. So, we need the amount of water in the tank to be **less than** the amount of water in the pool:
\[
1375 - 28x < 560x
\]

### Step 3: Simplify the inequality

Now, let's solve the inequality:
\[
1375 - 28x < 560x
\]
Add \( 28x \) to both sides to move all the terms involving \( x \) to one side:
\[
1375 < 588x
\]
Now, divide both sides by 588 to solve for \( x \):
\[
x > \frac{1375}{588} \approx 2.34
\]

### Conclusion:
The correct inequality is \( 1375 - 28x < 560x \), which corresponds to option **C**.

Would you like any further explanation or details on this solution?

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Here are 5 related questions:
1. How would the inequality change if the tank leaked at a different rate?
2. What happens if the pool fills faster than 560 gallons per hour?
3. How do you solve a system of inequalities with two variables?
4. How would you model the situation if the tank was being refilled while leaking?
5. How can you interpret the solution \( x > 2.34 \) in terms of time?

**Tip**: When solving inequalities, always be mindful of the direction of the inequality when multiplying or dividing by a negative number.

A tank starts off containing 1,375 gallons of water, and 28 gallons of water leaks from the tank every hour. At the same time, an empty pool is filled with water at a rate of 560 gallons per hour. Which inequality represents all possible values of x, the number of hours that have passed when the tank contains less water than the pool? A.1,375 + 28x > 560x B.1,375 – 28x > 560x C.1,375 – 28x < 560x D.1,375 + 28x < 560x

Learn how to solve an inequality involving a water tank losing water and a pool filling with water. This problem demonstrates how to compare linear equations and solve inequalities. Suitable for Grades 6-8 students.

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