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A 200-gallon tank is initially filled with 85 pounds of salt. Brine (salty water) enters with 0.10 lbs of salt per gallon at a rate of 10 gallons per minute. The mixture is kept thoroughly mixed and drained continuously at the same rate.

After 20 minutes, how much salt is in the tank?

Options:
A. 135 pounds
B. 165 pounds
C. 175 pounds
D. 185 pounds

Answer :

Final answer:

After 20 minutes, the tank will contain 105 pounds of salt.

Explanation:

To find out how much salt is in the tank after 20 minutes, we need to calculate the rate at which the salt enters and leaves the tank. The brine entering the tank has a salt concentration of 0.10 lbs per gallon, and it enters at a rate of 10 gallons per minute, so the rate of salt entering the tank is 0.10 lbs/gallon * 10 gallons/minute = 1 lb/minute.

Since the mixture is kept thoroughly mixed, the concentration of salt in the tank remains constant. Therefore, the rate of salt leaving the tank is the same as the rate of salt entering the tank, which is 1 lb/minute. After 20 minutes, the total amount of salt in the tank is 85 lbs (initial amount) + 1 lb/minute * 20 minutes = 85 lbs + 20 lbs = 105 lbs.

Therefore, the correct option is Option 4: 185 pounds.

Learn more about Calculating Salt Content here:

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