Question

A tank contains 600 gallons of a solution consisting of 100 lbs of salt dissolved in water. Salt solution with a concentration of 0.5 lb/gallon is added to the tank at a rate of 2 gallons per minute, and the mixture is drained from the tank at the same rate. What is the concentration of salt in the tank after 10 minutes?

Answer 1

The concentration of salt in the tank after 10 minutes is 0.1833 lb/gallon.

Step-by-step explanation:

The concentration of salt in the tank after 10 minutes can be calculated by considering the amount of salt added and the amount of water in the tank.

1. Initial concentration of salt in the tank = mass of salt / volume of water = 100 lbs / 600 gallons = 0.1667 lb/gallon
2. Rate of salt solution added = 2 gallons/minute
3. Rate of mixture drained from the tank = 2 gallons/minute
4. After 10 minutes, the total amount of salt added = 2 gallons/minute * 10 minutes * 0.5 lb/gallon = 10 lbs
5. The total volume of water in the tank after 10 minutes = initial volume + (rate of addition - rate of drainage) * time = 600 gallons + (2 gallons/minute - 2 gallons/minute) * 10 minutes = 600 gallons
6. Final concentration of salt in the tank after 10 minutes = total amount of salt / total volume of water = 110 lbs / 600 gallons = 0.1833 lb/gallon

Therefore, the concentration of salt in the tank after 10 minutes is 0.1833 lb/gallon.