A tank contains 3,000 L of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 5 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after 60 minutes?
Question
A tank contains 3,000 L of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 5 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after 60 minutes?
Solution
To solve this problem, we need to understand that the amount of salt in the tank is decreasing over time due to the inflow of pure water and the outflow of the saltwater mixture.
Here are the steps to solve the problem:
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First, we need to establish the rate at which the salt is leaving the tank. This is determined by the concentration of salt in the tank and the rate at which the solution is draining. The concentration of salt is the amount of salt divided by the volume of the solution, and the rate of draining is 5 L/min. So, the rate of salt leaving is (15 kg / 3000 L) * 5 L/min = 0.025 kg/min.
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Next, we need to determine how much salt is left in the tank after 60 minutes. Since the salt is leaving at a rate of 0.025 kg/min, after 60 minutes, the amount of salt that has left the tank is 0.025 kg/min * 60 min = 1.5 kg.
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Therefore, the amount of salt left in the tank after 60 minutes is the initial amount of salt minus the amount that has left, which is 15 kg - 1.5 kg = 13.5 kg.
So, there are 13.5 kg of salt left in the tank after 60 minutes.
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