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

Let's analyze the problem step by step to construct the correct inequality.

1. **Tank:**
   - The tank starts with 1,375 gallons of water.
   - It loses 28 gallons per hour.
   - After \( x \) hours, the amount of water left in the tank is:
     \[
     1,375 - 28x
     \]

2. **Pool:**
   - The pool starts empty and is being filled at a rate of 560 gallons per hour.
   - After \( x \) hours, the amount of water in the pool is:
     \[
     560x
     \]

3. **Condition:**
   - We want the tank to contain **less water** than the pool.
   - This gives the inequality:
     \[
     1,375 - 28x < 560x
     \]

4. **Rearranging the inequality:**
   - To match the options provided, we need to move all terms involving \( x \) to one side:
     \[
     1,375 < 560x + 28x
     \]
   - Simplifying:
     \[
     1,375 < 588x
     \]

Thus, the correct inequality is **\( 1,375 - 28x < 560x \)**, which corresponds to option **B**.

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Would you like more details on solving or graphing this inequality?

### Related questions:
1. How do you solve the inequality \( 1,375 - 28x < 560x \)?
2. After how many hours does the pool contain more water than the tank?
3. What is the meaning of the solution to the inequality in this context?
4. How do we solve systems of inequalities involving time and rates?
5. Can we use graphs to visualize the relationship between the tank and pool water levels?

**Tip:** When dealing with word problems, always start by translating the situation into algebraic expressions before solving.

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?

Learn how to solve the inequality involving a leaking tank and a filling pool. After x hours, the tank starts with 1,375 gallons and loses 28 gallons per hour, while the pool fills at 560 gallons per hour. Discover the step-by-step solution to find when the pool holds more water than the tank. Suitable for Grades 6-8.

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