What is the net gain of water in a tank after 5 minutes if it receives water at a rate of 120 gallons per minute and discharges water at 60 gallons per minute?

To determine the net gain of water in the tank after 5 minutes, we can begin by calculating the total amount of water being received and discharged during that time.

The tank receives water at a rate of 120 gallons per minute. Over a duration of 5 minutes, the total volume of water added to the tank is calculated as follows:

[

\text{Water In} = 120 \text{ gallons/min} \times 5 \text{ min} = 600 \text{ gallons}

]

In contrast, the tank discharges water at a rate of 60 gallons per minute. Therefore, during the same 5 minutes, the total volume of water discharged from the tank is:

[

\text{Water Out} = 60 \text{ gallons/min} \times 5 \text{ min} = 300 \text{ gallons}

]

To find the net gain in the tank, we subtract the total volume of water discharged from the total volume of water received:

[

\text{Net Gain} = \text{Water In} - \text{Water Out} = 600 \text{ gallons} - 300 \text{ gallons} = 300 \text{ gallons}