A tank initially contains 1 gram of blue dye dissolved in 10 liters of water. Pure water will be added to the tank at a certain rate, and the well-mixed solution will be drained from the tank at the same rate. The tank is considered “cleaned" when the dye concentration in the tank is no more than 0.001 grams/liter. (a) If the rate at which the pure water is added ( and the tank is drained) is 2 liters/ minute, how long does it take until the tank is clean? (b) If we want to clean the tank in 5 minutes, how quickly must the pure water be poured in?

A tank initially contains 1 gram of blue dye dissolved in 10 liters of water. Pure water will be added to the tank at a certain rate, and the well-mixed solution will be drained from the tank at the same rate. The tank is considered “cleaned" when the dye concentration in the tank is no more than 0.001 grams/liter. (a) If the rate at which the pure water is added ( and the tank is drained) is 2 liters/ minute, how long does it take until the tank is clean? (b) If we want to clean the tank in 5 minutes, how quickly must the pure water be poured in?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 45SE: A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the...

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Concept explainers

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.

Question

A tank initially contains 1 gram of blue dye dissolved in 10 liters of water. Pure water will
be added to the tank at a certain rate, and the well-mixed solution will be drained from
the tank at the same rate. The tank is considered “cleaned" when the dye concentration
in the tank is no more than 0.001 grams/liter.
(a) If the rate at which the pure water is added ( and the tank is drained) is 2 liters/
minute, how long does it take until the tank is clean?
(b) If we want to clean the tank in 5 minutes, how quickly must the pure water be poured
in?

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