Question

owners of a recreation area are filling a small pond with water. they are adding water at a rate of 32 liters per minute. there are 400 liters in the pond to start. let w represent the total amount of water in the pond (in liters), and let t represent the total number of minutes that water has been added. write an equation relating w to t. then use this equation to find the total amount of water after 12 minutes. equation: \\(\square\\) total amount of water after 12 minutes: \\(\square\\) liters

Explanation:

Step1: Form the equation

The initial amount of water is 400 liters, and water is added at a rate of 32 liters per minute. So the total amount of water \( W \) after \( T \) minutes is the initial amount plus the amount added in \( T \) minutes. The amount added in \( T \) minutes is \( 32T \) (since rate is 32 liters per minute). So the equation is \( W = 400 + 32T \).

Step2: Calculate water after 12 minutes

Substitute \( T = 12 \) into the equation \( W = 400 + 32T \). First, calculate \( 32 \times 12 \). \( 32\times12 = 384 \). Then add the initial 400 liters: \( W = 400 + 384 = 784 \).

Answer:

Equation: \( W = 400 + 32T \)
Total amount of water after 12 minutes: 784 liters