Water Tank A drains at a rate of 2 gallons an hour and has 240 gallons of water in it. Water Tank B fills at a rate of 0.5 gallons an hour and has 70 gallons of water in it. How long will it take before the two tanks contain the same amount of water? (Select all that apply)
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0 points
2x - 240 = 0.5 + 70x
240 - 2x = 0.5x + 70
240x - 2 = 0.5 + 70x
x = 68 hours
x = 9.5 hours

To solve this problem, let's first set up the correct equation based on the rates at which each tank is losing or gaining water.

### Define the variables:
- Let **x** represent the time (in hours) it will take for both tanks to have the same amount of water.

### Water Tank A:
- It starts with 240 gallons and **loses** water at a rate of 2 gallons per hour. After **x** hours, it will have:
  \[
  240 - 2x \text{ gallons}
  \]

### Water Tank B:
- It starts with 70 gallons and **gains** water at a rate of 0.5 gallons per hour. After **x** hours, it will have:
  \[
  70 + 0.5x \text{ gallons}
  \]

### Set up the equation:
We want to find when both tanks have the same amount of water, so we set the two expressions equal to each other:
\[
240 - 2x = 70 + 0.5x
\]

### Solve for x:
1. Subtract \(70\) from both sides:
   \[
   240 - 70 = 2x + 0.5x
   \]
   \[
   170 = 2.5x
   \]
2. Divide both sides by \(2.5\):
   \[
   x = \frac{170}{2.5} = 68 \text{ hours}
   \]

Thus, it will take **68 hours** for the two tanks to contain the same amount of water.

### Analyzing the provided options:

- The equation **"240 - 2x = 0.5x + 70"** is correct and matches the setup.
- The solution **"x = 68 hours"** is correct.

### Now, reviewing other options:
1. **"2x - 240 = 0.5 + 70x"** is incorrect because it does not match the correct form of the equation. The 70 should be a standalone term, not multiplied by x.
2. **"240x - 2 = 0.5 + 70x"** is also incorrect due to the improper placement of variables and terms.
3. **"x = 9.5 hours"** is incorrect because we solved for \(x = 68\) hours.

Would you like further clarification on any step?

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### Follow-up Questions:
1. What would the water levels in both tanks be after 68 hours?
2. How would the equation change if Tank B had an initial amount of 50 gallons?
3. How much water will be in Tank A after 30 hours?
4. How much water will be in Tank B after 100 hours?
5. If Tank A drained at a different rate, how would that affect the time to equal levels?

### Tip:
When solving word problems, clearly defining variables and setting up accurate equations is key to finding the solution.

Water Tank A drains at a rate of 2 gallons an hour and has 240 gallons of water in it. Water Tank B fills at a rate of 0.5 gallons an hour and has 70 gallons of water in it. How long will it take before the two tanks contain the same amount of water?

Learn how to solve a linear equation involving two water tanks, one draining and the other filling at different rates. This problem teaches key concepts like rates of change and setting up equations for equal conditions. Suitable for students in Grades 8-10.

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