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?

We are tasked with finding the inequality that represents the point at which the tank contains **less water** than the pool after a certain number of hours \( x \). Here's the breakdown:

### 1. Amount of water in the tank after \( x \) hours:
The tank starts with 1,375 gallons and leaks 28 gallons per hour. Therefore, the amount of water in the tank after \( x \) hours can be modeled by:

\[
\text{Water in tank} = 1375 - 28x
\]

### 2. Amount of water in the pool after \( x \) hours:
The pool starts empty and is filled at a rate of 560 gallons per hour. Therefore, the amount of water in the pool after \( x \) hours is:

\[
\text{Water in pool} = 560x
\]

### 3. Set up the inequality:
We want to know when the amount of water in the tank is **less** than the amount of water in the pool. This gives us the inequality:

\[
1375 - 28x < 560x
\]

### 4. Solve the inequality:

Step 1: Move all terms involving \( x \) to one side of the inequality:

\[
1375 < 560x + 28x
\]

Step 2: Simplify:

\[
1375 < 588x
\]

Step 3: Solve for \( x \):

\[
x > \frac{1375}{588} \approx 2.34
\]

Thus, the inequality representing all possible values of \( x \) when the tank contains less water than the pool is:

\[
x > \frac{1375}{588}
\]

This means that after approximately 2.34 hours, the tank will contain less water than the pool.

Would you like any further details or clarification on this?

Here are some related questions:
1. How does changing the leak rate affect the inequality?
2. What happens if the pool fills at a different rate?
3. What if the tank starts with a different amount of water?
4. How would the scenario change if both the tank and pool had initial amounts of water?
5. What happens when the rates of leakage and filling are equal?

**Tip:** Always check that the rates in these types of problems are correctly set up as positive for filling and negative for leaking.

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?

Discover how to solve an inequality involving a leaking tank and a filling pool. This problem demonstrates key algebraic concepts such as linear equations and properties of inequalities, ideal for students in Grades 8-10.

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