A mixer containing 100 gal of Na,SO, solution (4 lbs of Na2SO4 per gal) is attached to a reservoir containing a solution of 1 lb of Na,SO4/gal. If the solution is pumped from the reservoir at the rate of 5 gal/min and the mixed solution runs out of the mixer at the rate of 5 gal/min, how long will it take to reduce the concentration of salt in the tank to 1/2 its original value?

Q: A container initially contains 15 L of water in which there is 30 g of salt dissolved. A solution…

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Q: A tank contains initially 400 liters of brine holding 100 kg of salt in solution. Water containing…

A:

Q: A 200-gal tank is half full of distilled water. At time t=0, a solution containing 0.5 Ib/gal of…

A:

Q: 4. A large tank contains 100 gal of brine in which initially 50 lbs of salt are dissolved. Brine…

A:

Q: A tank initially contains 200 L of fresh water. Brine containing 2.5 N/L of dissolved salt runs into…

A: Let "s" represents the quantity of salt in the tank. dSdt=(8×2.5)-8S200dSdt+0.04S=20   and S(0)=0…

Q: A candy company wants to produce 25 kilograms of a special 35% fat content chocolate to conform with…

A: Given: A candy company wants to produce 25 kilograms of a special 35% fat content chocolate.To…

Q: In a mixing vat there are initially 100 litres of volatile liquid. 3 litres of fresh liquid are…

A: Solution

Q: A tank with a capacity of 5000 kg of water is initially half full. Twenty kilogram per minute is…

A: Given that the capacity of the tank is 5000 kg. Let Q be the quantity of water in the tank after t…

Q: If 10 pounds of salts is dissolved in a large tank in partially filled with 100 gallons of fluid.…

A: Given :   10 pounds of salts is dissolved in a large tank in partially filled with 100 gallons of…

Q: A 200-gal tank is half full of distilled water. At time t = 0, a solution containing 0.5 lb /gal of…

A: Given that the size of the tank is 200 gallon. Half of it is full, that means 200/2=100 gallon is…

Q: A sewage disposal plant has a big concrete holding tank of 100,000-gal capacity. It is % full of…

A: Let M(t) be the mass of the organic material in the tank at time t and Mt=CtVt, where C(t) and V(t)…

Q: at a rate proportional to the current population, and in the absence of other factors, the…

A: Consider at time t the population of mosquitoes is N in the area

Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: Given: The amount of water at 3:56 PM is 10452 L and amount of water at 4:12 PM on same day  is 8092…

Q: Tank A initially holds 100 gallons of brine that contains 150 pounds af salt, and tank B holds 100…

A: Tank A initially holds 100 gallons of brine that contains 150 pounds of salt.Tank B holds 100…

Q: A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a rate…

A: Solve by making differential equation

Q: A tank contains 400 liters of brine. Twelve (12) liters of brine, each containing 2.50 N of…

A: Given: 400 litres of brine are kept in a tank. The tank receives 12 litres of brine each minute,…

Q: A tank is initially filled with 1000 gal. of salt solution containing 500 H of salt. Fresh water…

A: Let At the amount of salt at the time t Then the rate of change of the amount of salt dAdt=0lbL.10…

Q: A 100-gallon tank contains 50 gallons of water. Brine, containing 2 lbs of salt per gallon, flows…

A: Given that, A 100-gallon tank contains 50 gallons of water. Brine, containing 2 lbs of salt per…

Q: There is a large mixing tank that initially holds 120 gallons of brine (water in which salt has been…

A:

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: Given :Half life of Palladium-100= 4 days

Q: A tank contains 80 galloons (gal) of pure water. A brine solution with 2 lb/gal of salt enters at 2…

A: Given that, A tank contains 80 galloons (gal) of pure water. A brine solution with 2 lb/gal of salt…

Q: A tank has 72 gallons of water. Brine solution with 2lbs of salt per gallon of solution enters at a…

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

Q: Tank A contains 274 litres of brine holding 123 N of dissolved salt, and tank B contains 274 litres…

A:

Q: Worker A is a loader and worker B is an unloader. Worker A can load a truck in 10mins, while worker…

A: The time taken by worker A to load the truck is = 10 min  The time taken by the worker B to unload…

Q: A tank contains 400 liters of brine. Twelve (12) liters of brine, each containing 2.5 N of dissolved…

A: If volume of any liquid is inside the container and some amount of liquid is entering and leaving…

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 2 grams…

A: A tank contains 200 liters of fluid with 30 gm salt is dissolved.2 gm of salt per liter is pumped…

Q: air containing 30% oxygen passes slowly into a 3 gallon flask initially filled with pure oxygen and…

A:

Q: If 150 g of copper at initial temperature of 50 °C gains 6930 J of heat when it is cooled to 170°C.…

A:

Q: A tank contains 80 gallons of pure water. A brine solution with 2lb/gal of salt enters at 2 gal/min,…

A: Given: r1=2 galsmin., r2=2 galsmin.,  c1=2 lbsgal,, v0=80 gallons, x0=0

Q: A 450 gal tank initially contains 110 gal of brine containing 52 Ib of salt. Brine containing 1lb of…

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Q: A tank with a capacity of 400 gal originally contains 150 gal of water with 25 lb of salt in…

A:

Q: A tank with a capacity of 400 gal originally contains 100 gal of water with 200 lb of salt in…

A: A tank with a capacity of 400 gal originally contains 100 gal of water with 200 lb of salt in…

Q: A tank contains 200 gallon of salt water with 150 lbs of dissolved salt. Salt water with 5 lbs of…

A:

Q: 1. A tank contains 80 gallons (gal) of pure water. A brine solution with 2 Ib/gal of salt enters at…

A: Given that, a tank contains 80 gallons (gal) of pure water. A brine solution with 2 lb/gal of salt…

Q: Two large tanks, each holding 24 liters of a brine solution, are interconnected by pipes as shown in…

A: Let x(t) and y(t) be the mass of salt in tanks T1 and T2 respectively. Fresh water follows into tank…

Q: A 500-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 2 Ib…

A: Given:   Equation data is given

Q: A 100 gallon tank is filled with brine containing 60 pounds of dissolved salt. Water runs into the…

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

Q: A tank contains 1000 liters of brine. Brine containing 0.4 kg/liter of salt flows in at 10…

A: Let st= The amount of salt at time t. The brine flows in at the rate 10 liters/minute and flows out…

Q: A 300 gallon tank initially contains 90 gallons of brine containing 400 Ibs. of salt. Brine…

A: Given the tank contains 90 gallons of brine containing 400 lbs of salt.  The above figure shows the…

Q: A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of…

A:

Q: A nurse gives 1,100 mL of an intravenous (IV) solution over a period of 9 h. It is given first at a…

A: Suppose, the time taken at a rate of 140 mL/h is x and the time taken at a rate of 100 mL/h is y.…

Q: We have a mixing tank that contains 100 gallons of water into which 5 pounds of sugar have been…

A: According to question. Initial amount of water in tank= 100gallons Initial amount of sugar = 5 pound

Q: A vessel with 500 gallons of beer contains 4% alcohol (by volume). Beer with 7% alcohol is pumped…

A:

Q: A 25-liter gas cylinder contains 80% oxygen and 20%   helium. If helium is added at a rate of 0.2…

A: The volume of cylinder =25 litre The percentage of oxygen in the cylinder initially=80% The amount…

Q: A 100L-capacity tank initially holds 80L of fresh water. A brine solution is poured into the tank at…

A: A brine solution is poured into the tank at the rate of 4 L/hr, while the well-stirred mixture…

Q: A tank contains 200 liters of fresh water. Brine containing 2.5 N/L of dissolved salt runs into the…

A:

Q: In a chemical reaction, substance A decomposes at a rate proportional to the amount of A present. It…

A: This decomposition reaction of first order, because rate is directly proportional to the…

Q: A tank contains 2000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

A:

Q: In a room containing of air 20,000 m3 of air, 600 m3 of fresh air flows in per minute, and the…

A:

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.