Brine from a first tank runs into a second tank at 2 gallons per minute and brine from the second tank runs into the first at 1 gallon per minute.Initially,there are 10 gallons of brine containing 20 lb of salt in the first tank and 10 gallons of fresh water in the second tank.How much salt will there be in the first tank after 5 minutes?
To solve this problem, let's break it down step by step.
Step 1: Determine the initial amount of salt in each tank.
In the first tank, there are 10 gallons of brine containing 20 lb of salt.
In the second tank, there are 10 gallons of fresh water, which means there is no salt.
Step 2: Calculate the rate of salt transfer between the tanks.
The first tank receives brine from the second tank at a rate of 1 gallon per minute. This brine has no salt, so it doesn't affect the amount of salt in the first tank.
The first tank transfers brine to the second tank at a rate of 2 gallons per minute. This brine contains salt from the first tank, which will increase the amount of salt in the second tank.
Step 3: Calculate the amount of salt transferred from the first tank to the second tank.
Since the brine transfer rate is 2 gallons per minute, in 5 minutes, 5 * 2 = 10 gallons of brine will be transferred from the first tank to the second tank. Since the brine from the first tank has 20 lb of salt, the second tank will receive 20 lb of salt.
Step 4: Calculate the amount of salt remaining in the first tank.
Since the first tank transfers 2 gallons of brine per minute, in 5 minutes, it will transfer 5 * 2 = 10 gallons of brine. This means that the first tank will be empty after 5 minutes, and there will be no salt remaining in it.
Step 5: Calculate the total amount of salt in the system after 5 minutes.
The second tank initially has no salt, but it receives 20 lb of salt from the first tank. Therefore, after 5 minutes, the second tank will have a total of 20 lb of salt.
So, after 5 minutes, there will be 20 lb of salt in the first tank and 20 lb of salt in the second tank.