Question

A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute. Let w = quarts of water left in the tub and t = time in minutes.

A 2-column table with 3 rows. The first column is labeled time (t) with entries 0, 2, 4. The second column is labeled quarts of water (W) with entries 50, 45, 40.

Choose the correct answers.

Which equation models the relationship?

Is there a viable solution when time is 30 minutes?

Answer 1

To model the relationship between the amount of water left in the tub (w) and time (t), we can start with the initial amount of water and subtract the amount that has drained over time.

1. **Equation**:
The tub starts with 50 quarts of water and empties at a rate of 2.5 quarts per minute. The equation that describes the relationship is:

\[
w = 50 - 2.5t
\]

2. **Viable Solution**:
To determine if there is a viable solution when time (t) is 30 minutes, we can substitute 30 into the equation:

\[
w = 50 - 2.5(30)
\]
\[
w = 50 - 75
\]
\[
w = -25
\]

Since the result is -25 quarts, this is not a viable solution—because you cannot have a negative amount of water in the tub. Thus, at 30 minutes, the tub would have already emptied (at exactly 20 minutes, it becomes empty, since \( 50 / 2.5 = 20 \)). So, the answer is:

- **Equation**: \( w = 50 - 2.5t \)
- **Viable Solution when t = 30?**: No, it is not viable since it results in a negative amount of water.