1. A tank initially contains 40 pounds of salt dissolved in 100 gallons water. A solution containing 0.05 pounds of salt per gallon runs into the tank at 4 gallons per minute and the well-stirred solution runs out at 2 gallons per minute. How long will it be until there are 30 pounds of salt in the tank? What is the limiting amount of salt in the tank after a very long time?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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After about 29.3 minutes and again after about 170.7 minutes; the amount of salt approaches ∞ after a

very long time (we’ll assume the tank can hold the infinite volume since we weren’t told the size of the

tank)

11. A tank initially contains 40 pounds of salt dissolved in 100 gallons water. A solution containing 0.05
pounds of salt per gallon runs into the tank at 4 gallons per minute and the well-stirred solution runs out
at 2 gallons per minute. How long will it be until there are 30 pounds of salt in the tank? What is the
limiting amount of salt in the tank after a very long time?
Transcribed Image Text:11. A tank initially contains 40 pounds of salt dissolved in 100 gallons water. A solution containing 0.05 pounds of salt per gallon runs into the tank at 4 gallons per minute and the well-stirred solution runs out at 2 gallons per minute. How long will it be until there are 30 pounds of salt in the tank? What is the limiting amount of salt in the tank after a very long time?
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