If an ion exchange softener treats a flow rate of 125 gpm, how many hours does it operate if it treats 297,000 gallons before regeneration?

To determine how many hours the softener operates before regeneration, you first need to calculate the total time it can treat water based on the given flow rate and the total volume treated.

The formula to find the time in hours is:

[

\text{Time (hours)} = \frac{\text{Total Volume (gallons)}}{\text{Flow Rate (gpm)} \times 60}

]

In this case, the total volume is 297,000 gallons, and the flow rate is 125 gallons per minute.

First, find the total treatment time in minutes:

[

\text{Time (minutes)} = \frac{297,000 \text{ gallons}}{125 \text{ gpm}} = 2,376 \text{ minutes}

]

Next, convert that time from minutes to hours by dividing by 60:

[

\text{Time (hours)} = \frac{2,376 \text{ minutes}}{60} = 39.6 \text{ hours}

]

Thus, the softener operates for 39.6 hours before needing regeneration. This calculation clearly supports the choice, as it accurately relates the total gallons treated to the consistent flow rate at which