A bathtub is filled with 40 gallons of water. The water starts draining out of the tub at 8 gallons per minute. Put the scenario into linear equation form.

Answer 1

To set up a linear equation for the scenario described, we can define the variables and the relationship between them.

Let:

• \( t \) be the time in minutes after the water starts draining.
• \( W(t) \) be the amount of water in gallons remaining in the bathtub after \( t \) minutes.

The bathtub starts with 40 gallons of water. Since the water drains at a rate of 8 gallons per minute, the amount of water remaining after \( t \) minutes can be represented by the equation:

\[ W(t) = 40 - 8t \]

Here, \( W(t) \) decreases linearly over time \( t \) due to the steady rate of water draining. This equation shows that initially (when \( t = 0 \)), there are 40 gallons (\( W(0) = 40 \)), and with each passing minute, 8 gallons are subtracted from the total.