Time to Fill Tank with 450 Gallons

To determine the time it will take for the water tank to hold 450 gallons of water, we'll start with the information given: - The tank initially contains 300 gallons of water. - Water is being pumped into the tank at a rate of 9 gallons per minute. We need to find how many minutes, \( t \), it will take for the tank to go from 300 gallons to 450 gallons. First, calculate the required increase in the amount of water: \[ 450 \text{ gallons} - 300 \text{ gallons} = 150 \text{ gallons} \] Next, use the rate at which water is being pumped into the tank to determine the time. The rate is 9 gallons per minute, so we set up the equation: \[ \text{Increase in water} = \text{Rate} \times t \] \[ 150 \text{ gallons} = 9 \text{ gallons/min} \times t \] Now, solve for \( t \): \[ t = \frac{150 \text{ gallons}}{9 \text{ gallons/min}} \] \[ t = \frac{150}{9} \] \[ t \approx 16.67 \text{ minutes} \] Therefore, it will take approximately 16.67 minutes for the tank to contain 450 gallons of water.