A tank contains a solution of saltwater, where the concentration of salt changes over time as the tank is being filled and drained simultaneously. The volume of the solution is increasing at a constant rate of 0.5 liters per minute. The amount of salt (in pounds) is always 1/3 of the total volume of solution in the tank. How fast is the amount of salt (in pounds) increasing or decreasing after 5 minutes?

Q: For a certain square, the side is increasing at the rate of 2 mm/s. At what rate is the perimeter of…

A: We know       Perimeter (P) = 4 × ( side of square)

Q: A tank contains (400 L) of brine made by dissolving (20 kg) of salt in water. Salt water containing…

A: dVindt = 2 L/min       (Volume in rate)dVoutdt = 5 L/min    (Volume out rate)Therefore, Net  dVdt =…

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A: Find the base where area and altitude is already given, then the formula of the area of a triangle…

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.