A 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 1 lb of salt per gallon enters the tank at the rate of 5 gal/s, and the well-mixed brine in the tank flows out at the rate of 3 gal/s. How much salt will the tank contain when it is full of brine?

Q: A tank is filled with 400 gallons of brine with 25 % dissolved salt. 5 gallons of 20% salt solution…

A:

Q: d) An 800-liter tank is half full of water is being filled with water pumped at the rate of 45…

A: We have, an 800-liter tank is half full of water and is being filled with water pumped at the rate…

Q: A tank is filled with 400 gallons of brine with 15 % dissolved salt. 10 gallons of 20% salt solution…

A: Given datavolume of tank=400 gallonsAmount of salt=15% of 400=400*15100=60

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

A: Solution

Q: A 600 gallon brine tank is to be cleared by piping in pure water at 1 gal/min. , and allowing the…

A: Let S be pounds of salt in tank at time t, so: or Rewritting the equation above we get:…

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)…

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Q: In order to stay awake during class, a professor keeps a 200 ounce capacity coffee maker in his…

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Q: A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to…

A: A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to…

Q: a 400 gal tank initially contains 100 gal of brine containing 25 lb of salt. Brine containing 2 lb…

A: A real-life scenario can be described mathematically through a differential equation. By solving the…

Q: A truck gets 600/x miles per gallon when driven at a constant speed of x mph, where 40 < x <…

A: It can go 600/x miles in 1 gallon. And cost  of 1 gallon is 2.80.So cost for (600/x) miles =…

Q: brandon walks 3 miles at a certain speed and then he jobs 3 moles per hour faster for 9 miles. If…

A:

Q: At 9 p.m., a cylinder containing 240 liters of brine in which 12kg of salt is dissolved. Brine…

A: We will find how much salt in the cylinder is by 9.30

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

A:

Q: The rate at which the body cools is proportional to the difference in temperature of the body and…

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Q: If a machine that works at a constant rate can fill 40 bottles of milk in 3 minutes, how many…

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Q: In a city with 500,000 population, the rate of the spread of a new flu epidemic is proportional to…

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Q: An automobile uses gasoline at a rate of 12 kilometres per litre and has a 65 litre tank. How far…

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Q: A large tank initially contains 50 liters of brine in which there is dissolved 5 grams of salt.…

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Q: A motor vehicle has a maximum efficiency of 32 mpg at a cruising speed of 40 mph. The efficiency…

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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: A certain drug breaks down in the body at a rate of 18% per hour. If an initial dosage is 500…

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Q: A van is 5km due north of a bus at 2:00PM. If the van is traveling northward at the rate of 60 kph…

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Q: Juan's body metabolizes caffeine at a rate of 14.2% per hour (so the amount of caffeine in Juan's…

A: Given: Juan's body metabolizes caffeine at a rate of 14.2% per hour. Also, Juan consumes a cup of…

Q: A scuba tank holds 2.6 ㎥ of compressed air. A diver at a shallow depth uses about 0.002 ㎥ per breath…

A: Total compressed air in scuba tank = 2.6 m^3 Compressed air used per breath is 0.002 m^3 Breath…

Q: There are 100 bacteria cells in a dish now, but in 5 hours there will be 147 cells. At what rate do…

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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 group of fitness club members lose a combined total of 28 kilograms in 1 week. There are…

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Q: A bunch of hooligans dump 164 pounds of  pizza boxes into a lake. If the pizza boxes dissipates at a…

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Q: A tank contains 100 L of water. A salt solution containing 2 kg of salt per liter flow in at the…

A:

Q: A tank contains 1,000 gallons of brine in which 500 lbs of salt are dissolved. Fresh water runs into…

A: Given:-amount of brine in the tank=1000 gallonssalt are dissolved in brine=500 lbsrate of fresh…

Q: 10 liters per​ minute, how long will it take to fill the 3,400​-gallon ​pool?

A:

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 120-gallon tank initially contains 80 lbs. of salt dissolve in 90 gal of water. Brinemcontaining…

A: Let xt be the amount of salt in tank at time t.  The amount of salt in is given by salt in=10 The…

Q: How long will it take to purge a 15ft section of 6in pipe with a flow rate of 35cfh

A: Given information Length of the section L=15 ft=15×12=180 in Hence, L=180 in Diameter of the pipe is…

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

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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: One mole of gas expands isothermically to double its volume. If the gas temperature is 340 k what…

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Q: Aman invested $20,000 in the bank. Apart of it was invested at 5% and the rest at 10%. The total…

A: total amount invested $20,000 and consider the time is 1 years for which the money is invested  Let…

Q: 600 gallon brine tank is to be cleared by piping in pure water at 1 gal/min. , and allowing the…

A:

Q: A 400-gallon tank initially contains 100 gallons of brine containing 50 pounds of salt. Brine…

A: Formulate a differential equation as follows. Let A(t) be the rate of change of amount of salt in…

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Q: A patient is drinking  0.6 pint of orange juice every two hours. At this rate, how many quarts of…

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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.