Container A has 200 L of water and is  being filled at a rate of 6 liters per minute.Container B has 500 L of water and is being  drained at 6 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water

Let's define the problem with equations to represent the amount of water in each container over time.

### Container A:
- Initially, it has 200 liters of water.
- It's being filled at 6 liters per minute.
- After \( m \) minutes, the amount of water in Container A will be:
  \[
  \text{Water in A} = 200 + 6m
  \]

### Container B:
- Initially, it has 500 liters of water.
- It's being drained at 6 liters per minute.
- After \( m \) minutes, the amount of water in Container B will be:
  \[
  \text{Water in B} = 500 - 6m
  \]

### Find when the two containers have the same amount of water:
We set the two expressions equal to each other:
\[
200 + 6m = 500 - 6m
\]

### Solve for \( m \):
1. Combine like terms by adding \( 6m \) to both sides:
   \[
   200 + 6m + 6m = 500
   \]
   \[
   200 + 12m = 500
   \]

2. Subtract 200 from both sides:
   \[
   12m = 300
   \]

3. Divide both sides by 12:
   \[
   m = \frac{300}{12} = 25
   \]

Thus, it will take **25 minutes** for both containers to have the same amount of water.

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Would you like more details or have any questions on this solution? 

Here are 5 relative questions to explore further:

1. How would the solution change if Container A had a different initial volume of water?
2. What happens if both containers are filled at different rates?
3. What if Container B was draining at a slower rate than Container A was being filled?
4. How would you model this problem graphically?
5. How can we generalize this problem to account for other filling and draining rates?

**Tip:** When solving problems with time-dependent rates, it's helpful to first express everything in terms of a single variable and write clear equations.

Container A has 200 L of water and is being filled at a rate of 6 liters per minute. Container B has 500 L of water and is being drained at 6 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water?

Explore how to solve a real-world problem involving water flow rates. Learn how to calculate when two containers, one being filled and one being drained, will have the same amount of water using linear equations. Suitable for students in Grades 6-8.

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