a bathtub was filled with 40 gallons of water when the drain was pulled to empty the tub. The table shows how much water was left in the tub at certain times since the plug was pulled. assuming the tub drains at a constant rate, about how many minutes will it take until it is empty

To determine how many minutes it will take until the bathtub is empty, we need to analyze the data provided and establish the rate at which the tub is draining.

Let's assume the table looks something like this:

| Time (minutes) | Water left (gallons) |
|----------------|----------------------|
| 0              | 40                   |
| 5              | 30                   |
| 10             | 20                   |
| 15             | 10                   |

From the table, we can see that every 5 minutes, the amount of water decreases by 10 gallons. This implies a constant rate of drainage.

### Step-by-Step Solution:

1. **Determine the rate of drainage:**
   - From 40 gallons to 30 gallons in 5 minutes: \(40 - 30 = 10\) gallons in 5 minutes.
   - Therefore, the rate is \(\frac{10 \text{ gallons}}{5 \text{ minutes}} = 2 \text{ gallons per minute}\).

2. **Calculate the total time to empty the tub:**
   - The tub starts with 40 gallons.
   - At a rate of 2 gallons per minute, we need to find the time \( t \) when the tub will be empty.
   - Using the formula \( \text{Time} = \frac{\text{Total water}}{\text{Rate}} \):
   \[
   \text{Time} = \frac{40 \text{ gallons}}{2 \text{ gallons per minute}} = 20 \text{ minutes}
   \]

### Conclusion:
It will take 20 minutes for the bathtub to be completely empty.

Do you have any questions or would you like more details?

Here are 5 questions you might consider next:
1. How can I find the rate of change from a different data set?
2. What if the rate of drainage was not constant? How would the approach change?
3. How can I apply this method to different real-world scenarios?
4. Can you explain more about interpreting tables in algebra?
5. What other methods can be used to solve similar rate problems?

**Tip:** When working with rates, always check if the rate is constant or variable, as it affects how you approach the problem.

Discover how to calculate the time needed to empty a bathtub filled with 40 gallons of water at a constant drainage rate. Our detailed solution shows that it takes 20 minutes to drain the tub, utilizing the rate of 2 gallons per minute.

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