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Beginning at time t = 0, fresh water is pumped at the rate
Chapter 3, Problem 7E(choose chapter or problem)
Problem 7E
Problem
Beginning at time t = 0, fresh water is pumped at the rate of 3 gal/min into a 60-gal tank initially filled with brine. The resulting less-and-less salty mixture overflows at the same rate into a second 60-gal tank that initially contained only pure water, and from there it eventually spills onto the ground. Assuming perfect mixing in both tanks, when will the water in the second tank taste saltiest? And exactly how salty will it then be, compared with the original brine?
Questions & Answers
QUESTION:
Problem 7E
Problem
Beginning at time t = 0, fresh water is pumped at the rate of 3 gal/min into a 60-gal tank initially filled with brine. The resulting less-and-less salty mixture overflows at the same rate into a second 60-gal tank that initially contained only pure water, and from there it eventually spills onto the ground. Assuming perfect mixing in both tanks, when will the water in the second tank taste saltiest? And exactly how salty will it then be, compared with the original brine?
ANSWER:
Solution:
Step 1:
Give x1(t) a chance to be the measure of salt at time t in tank 1.
The rate of new water going into the tank at first is 3 gals/min.
The volume of water in tank 1 is a consistent 60 gals, at that point to get
= (Rate water enters tank 1) - (Rate water leaves tank 1)
= 0 *3 -
=
=