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.