Final answer:
To determine the number of gallons of water that can be softened before the softener requires regeneration, calculate the total hardness removal capacity of the resin and compare it to the hardness of the water being treated. Approximately 59.92 gallons of water can be softened before the softener will require regeneration.
Step-by-step explanation:
To determine how many gallons of water can be softened before the softener requires regeneration, we need to calculate the total hardness removal capacity of the resin and compare it to the hardness of the water being treated.
The resin has a hardness removal capacity of 25 kilograins per cubic foot.
Given that there are 35 cubic feet of resin in the softener, the total hardness removal capacity is 35 x 25 = 875 kilograins.
The water being treated has a hardness of 250 milligrams per liter as CaCO3.
To convert this to kilograins, we can use the conversion factor 1 kilograin = 64.8 milligrams. So, 250 milligrams per liter is equivalent to 250 / 64.8 = 3.86 kilograins per liter.
Now, to find the number of gallons of water that can be softened, we divide the total hardness removal capacity by the hardness of the water:
875 kilograins / 3.86 kilograins per liter = 226.75 liters.
Since 1 liter is equal to 0.2642 gallons, the number of gallons of water that can be softened is approximately 226.75 x 0.2642 = 59.92 gallons.