Final answer:
To find the total amount of salt in a tank after t minutes, calculate the amount of salt added per minute and subtract the amount drained per minute. Multiply this by t to determine the change in the tank's salt content. Consider the initial salt mass, the concentration of the incoming salt solution, and the flow rate in your calculations.
Step-by-step explanation:
Calculating the Total Amount of Salt in a Tank Over Time
The problem involves a tank where a salt solution is added at a certain rate and is mixed and drained at the same rate. To find the total amount of salt in the tank after time t minutes, we need to know the initial amount of salt in the tank, the concentration of salt in the entering solution, and the rate at which the solution is added and drained. Using the principles of molarity calculations, we can determine the changes in the concentration of salt over time. First, calculate the amount of salt added per minute, then calculate the amount of salt leaving the tank per minute. The change in salt content over one minute will be the amount added minus the amount drained. Multiplying this change by t will give the net amount of salt added to or removed from the initial salt mass over the time period of t minutes.
To illustrate, let's assume you have an initial amount of salt in the tank, a concentration of salt in the incoming solution, and a flow rate. For simplicity, let's say there are initially 100 kg of salt in the tank, and the concentration of the incoming solution is 5 kg of salt per liter (5 kg/L). If the solution enters the tank at 1 L/min and is mixed and drained at the same rate, you're adding 5 kg of salt to the tank every minute. As saltwater is also being drained at 1 L/min, you need to adjust the total amount of salt based on the total volume of the solution in the tank, which is becoming more concentrated with salt from the incoming solution.