Question

A tank initially contains 200 gallons of brine, with 50 pounds of salt in solution. Brine containing 2 pounds of salt per gallon is entering the tank at the rate of 4 gallons per minute and is is flowing out at the same rate. If the mixture in the tank is kept uniform by constant stirring, find the amount of salt in the tank at the end of 40 minutes.

Answer 1

The amount of salt in the tank at the end of 40 minutes is 370 pounds.

Step-by-step explanation:

To find the amount of salt in the tank after 40 minutes, we need to calculate the net change in the amount of salt in the tank during that time. The tank initially contains 200 gallons of brine with 50 pounds of salt, and brine is flowing in and out of the tank at a rate of 4 gallons per minute. Since the salt concentration in the brine entering the tank is 2 pounds per gallon, the amount of salt entering the tank each minute is 4 gallons x 2 pounds = 8 pounds.

Therefore, the net change in the amount of salt in the tank after 40 minutes is 40 minutes x 8 pounds/minute = 320 pounds. Adding this to the initial amount of salt in the tank, we get 50 pounds + 320 pounds = 370 pounds of salt in the tank at the end of 40 minutes.

Answer 2

y = 50

t=0

we find at end of 40 minutes value of salt is y = 242.735

Step-by-step explanation:

explanation has been defined in attachment