Question

A tank initially contains 50 gallons of pure water. Starting at t = 0, a brine containing 2 lb of dissolved salt per gallon flows into the tank at a rate of 3 gal./min. The mixture is kept uniform by stirring, and the well-stirred mixture simultaneously flows out of the tank at the same rate. How much salt is in the tank at any time t?

Name: a tank initially contains 50 gallons of pure water starting at t 0 a brine containing 2 lb of dissolved salt per gallon flows into the tank at the rate of 3 galmin the mixture is kept unifor 46383
Uploaded: 2022-08-12T16:34:59-08:00
Duration: 3 min 22 s
Channel: Vishal Parmar
Description: a tank initially contains 50 gallons of pure water starting at t 0 a brine containing 2 lb of dissolved salt per gallon flows into the tank at the rate of 3 galmin the mixture is kept unifor 46383

          A tank initially contains 50 gallons of pure water. Starting at t = 0, a brine containing 2 lb of dissolved salt per gallon flows into the tank at a rate of 3 gal./min. The mixture is kept uniform by stirring, and the well-stirred mixture simultaneously flows out of the tank at the same rate. How much salt is in the tank at any time t?

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Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vishal Parmar

08/12/2022

Step 1

Let \( S(t) \) be the amount of salt in the tank at time \( t \) in pounds. The rate at which the brine enters the tank is 3 gallons per minute, each gallon containing 2 pounds of salt. Therefore, the rate of salt entering the tank is \( 2 \times 3 = 6 \) pounds Show more…

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A tank initially contains 50 gallons of pure water. Starting at t = 0, a brine containing 2 lb of dissolved salt per gallon flows into the tank at a rate of 3 gal./min. The mixture is kept uniform by stirring, and the well-stirred mixture simultaneously flows out of the tank at the same rate. How much salt is in the tank at any time t?