Two connected tanks, each with a capacity of 50 liters, contain brine (saltwater). Initially, the first tank contains 18 liters of brine with a salt concentration of 3 grams per liter and the second contains 17 liters of brine with a salt concentration of 2 grams per liter. At t = 0 brine with a salt concentration of 6 grams per liter flows into the first tank at 8 liters per hour. Well-stirred brine flows from the first tank into the second at 7 liters per hour, from the second into the first at 5 liters per hour, from the first into a drain at 4 liters per hour, and from the second into a drain at 3 liters per hour. (a) Determine the volume (liters) of brine in each tank as a function of time. (b) Give an initial-value problem that governs the amount (grams) of salt in each tank as a function of time. (c) Give the interval of definition for the solution of this initial-value problem.
Two connected tanks, each with a capacity of 50 liters, contain brine (saltwater). Initially, the first tank contains 18 liters of brine with a salt concentration of 3 grams per liter and the second contains 17 liters of brine with a salt concentration of 2 grams per liter. At t = 0 brine with a salt concentration of 6 grams per liter flows into the first tank at 8 liters per hour. Well-stirred brine flows from the first tank into the second at 7 liters per hour, from the second into the first at 5 liters per hour, from the first into a drain at 4 liters per hour, and from the second into a drain at 3 liters per hour.
(a) Determine the volume (liters) of brine in each tank as a function of time.
(b) Give an initial-value problem that governs the amount (grams) of salt in each
tank as a function of time.
(c) Give the interval of definition for the solution of this initial-value problem.
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