Question

3. consider a system of two well-stirred and interconnected tanks that are filled to ca- pacity. tank 1 holds 24 litters of water, initially containing 10 kg of salt. tank 2 also holds 24 litters of water, initially containing 4 kg of salt. fresh water flows into tank 1 at a rate of 6 litters per minute while salt solution flows out of tank 2 at the same rate of 6 litters per minute. salt solution is pumped from tank 1 to tank 2 at the rate of 8 litters per minute and salt solution is pumped from tank 2 to tank 1 at the rate of 2 litters per minute. find the amount of salt in each tank after 10 minutes. round your answer to two decimal places.

Answer 1

After 10 minutes, there is no salt left in Tank 1 and there is 204 kg of salt in Tank 2.

Step-by-step explanation:

To find the amount of salt in each tank after 10 minutes, we need to consider the inflow and outflow of salt solution in both tanks.

In 10 minutes, tank 1 receives fresh water at a rate of 6 liters per minute, which means it receives 6 * 10 = 60 liters of fresh water. The salt solution is pumped from tank 1 to tank 2 at a rate of 8 liters per minute, which means tank 1 loses 8 * 10 = 80 liters of salt solution.

In tank 2, the salt solution flows out at a rate of 6 liters per minute, so in 10 minutes, it loses 6 * 10 = 60 liters of salt solution. The salt solution is pumped from tank 2 to tank 1 at a rate of 2 liters per minute, which means tank 2 loses 2 * 10 = 20 liters of salt solution.

Now, let's calculate the amount of salt in each tank:

Amount of salt in tank 1 = 10 kg + (60 liters * 0 kg/liter) - (80 liters * 10 kg/liter) = 10 kg - 800 kg = -790 kg (There is no salt left in tank 1 after 10 minutes)

Amount of salt in tank 2 = 4 kg + (60 liters * 10 kg/liter) - (60 liters * 10 kg/liter) + (20 liters * 10 kg/liter) = 4 kg + 600 kg - 600 kg + 200 kg = 204 kg