Question
Asked Jan 24, 2019
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A tank holds 100 gal of a water-salt solution in which 4.0 lb of salt is dissolved. Water runs into the tank at the rate of 5 gal/min and salt solution overflows at the same rate. If the mixing in the tank is adequate to keep the concentration of salt in the tank uniform at all times, how much salt is in the tank at the end of 50 min? Assume that the density of the salt solution is essentially the same as that of water.

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Expert Answer

Step 1

Let the function for amount of salt (kg) in the tank at time ‘t’ minutes be, S(t).

Now, the rate of change of the amount of salt in the tank will be S’(t). This is defined as:

S’(t) = (rate of salt going in the tank) – (rate of salt going out of the tank)                …… (1)

Step 2

Pure water flows inside the tank at the rate of 5 gal/min. The rate of salt going in the tank is given by equation (2) as:

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Step 3

The rate of salt solution flowing out the tank is same as that of the pure water flowing in the tank. The concentration of the salt solution flowing out of the t...

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