Final answer:
The steady-state concentration of the salt in the tank does not match any of the given options. The calculation leads to a concentration of 13.33 lbs/gal, which suggests there might be an error in the provided options.
Step-by-step explanation:
The problem you're describing is a differential equation model for the mixing of solutions. At the start, the tank contains 1,000 gallons of water with 300 lbs of salt. As the brine solution with a concentration of 10 lbs/gal enters the tank at 20 gal/min and the mixture leaves the tank at 15 gal/min, the concentration of the salt in the tank changes over time. To find the steady-state concentration of salt in the tank, if such a state exists, we need to set the rates of salt entering and leaving the tank equal.
The rate at which salt enters is 200 lbs/min (10 lbs/gal times 20 gal/min), and the rate at which salt leaves is the concentration in the tank (c lbs/gal) times the outflow rate (15 gal/min). At steady state, these rates are equal:
200 lbs/min = 15 gal/min * c lbs/gal
Solving for c gives us:
c = 200 lbs/min / 15 gal/min = 13.33 lbs/gal
This value does not match any of the options given (a-d). Therefore, there may be an error in the problem statement or the options provided. It is possible that in a real-world scenario, the brine concentration in the outflow would eventually reach a steady state, but this state is not represented by the options given.