Answer:To solve this problem, let's calculate the mass of salt in the tank after 10 minutes.
We can break down the problem into two parts: the salt that was initially in the tank and the salt that entered or left the tank during the 10 minutes.
Salt initially in the tank:
The initial mass of salt in the tank is 100 kg multiplied by the concentration of salt in the brine, which is 60% or 0.6.
Initial salt in the tank = 100 kg * 0.6 = 60 kg.
Salt entering the tank:
The inlet stream brings in 10 kg/min of a 10% brine solution. We need to calculate the mass of salt in this stream.
Salt entering the tank per minute = 10 kg * 0.1 = 1 kg/min.
Since the inlet stream flows for 10 minutes, the total mass of salt entering the tank during this period is:
Salt entering the tank = 1 kg/min * 10 min = 10 kg.
Salt leaving the tank:
The drain stream removes 15 kg/min from the tank. However, since the concentration of salt in the tank is not specified, we can assume that the concentration of salt in the drain stream is the same as the concentration of the tank's contents.
Salt leaving the tank per minute = Concentration of salt in the tank * Drain stream rate = 0.6 * 15 kg/min = 9 kg/min.
Since the drain stream also operates for 10 minutes, the total mass of salt leaving the tank during this period is:
Salt leaving the tank = 9 kg/min * 10 min = 90 kg.
Calculation of final salt mass:
To find the final mass of salt in the tank after 10 minutes, we need to add the initial salt in the tank, the salt entering the tank, and subtract the salt leaving the tank.
Final salt in the tank = Initial salt in the tank + Salt entering the tank - Salt leaving the tank
Final salt in the tank = 60 kg + 10 kg - 90 kg
Final salt in the tank = -20 kg.
The result, -20 kg, indicates that the tank has a deficit of 20 kg of salt after 10 minutes, which means there is not enough salt to maintain the specified concentrations.
Step-by-step explanation: