A large tank contains 100 gallons of brine in which 10 lbs. of salt is dissolved. Brine containing 0.2 lbs. of salt to the gallon runs into the tank at the rate of 6 gal/min. The mixture, kept uniform by stirring, runs out of the tank at the rate of 4 gal/min. Find the amount of salt in the solution in the tank at the end of t min.

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A: Please refer to the image below

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Q: Initially a tank holds 100 gal of a brine solution containing 4 lb of salt. At t = 0, brine…

A: We will find out the required time.

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A: here we can use differential equation to solve this question.

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A:

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A: 1 hour is equal to 60 minutes.

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A:

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A: Form the differential equation of first order and solve to get the answer.

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A: Remaining capacity of tank is 50-10 = 40 gallons.

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Q: Consider two brine tanks connected as shown in the figure below. Tank 1 contains x(t) pounds of salt…

A: Since there is no image for flow in the tanks, i use only the given equation with initial values.

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Q: A tank contains 1000 liters (L) of a solution consisting of 195 kg of salt dissolved in water. Pure…

A: Solution is given below:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.