You have a shortage of drinkable water in your town and are trying to prepare safe drinking water by mixing river water with concentrated sea water. A tank initially has S0 amount of salt mixed in 1000 liters of water in it. River water enters the tank at a rate of r liters/h and the salt concentration of this water is 0.01 g/liter. Assume that the water salt mixture is well-stirred. It is also given that water is drained from the tank at the same rate as it comes in.(a) Find the differential equation which describes this scenario. You must explain in your own words and logically derive the equation.(b) Solve for S (t) in terms of r, So and t(time in hours).(c) New York's department of health recommends that salt concentration should not exceed 0.02 g/liter for the water to be drinkable. Given that, initially the sea water contains 35 g/liter liters of salt. You keep measuring the amount of salt in the tank and note that after a while it is no longer changing significantly. What is the amount of salt now ? Calculate the salt concentration and comment on whether the water in the tank is safe to drink.(d) The town provides you with industrial motors which pumps river water into the tank at a rate r = 100 liters/h. How long does it take for sea water in the tank to become just drinkable ?(e) Comment on what would happen if your motors were more powerful. 1. You have a shortage of drinkable water in your town and are trying to preparesafe drinking water by mixing river water with concentrated sea water. A tankinitially has So amount of salt mixed in 1000 liters of water in it. River waterenters the tank at a rate of r liters/h and the salt concentration of this wateris 0.01 g/liter. Assume that the water salt mixture is well-stirred. It is alsogiven that water is drained from the tank at the same rate as it comes in.00rliters/n(a) Find the differential equation which describes this scenario. You mustexplain in your own words and logically derive the equation.(b) Solve for S (t) in terms of r, So and t(time in hours).(c) New York's department of health recommends that salt concentrationshould not exceed 0.02 g/liter for the water to be drinkable. Giventhat, initially the sea water contains 35 g/liter liters of salt. You keepmeasuring the amount of salt in the tank and note that after a while itis no longer changing significantly. What is the amount of salt now ?Calculate the salt concentration and comment on whether the water inthe tank is safe to drink.(d) The town provides you with industrial motors which pumps river waterinto the tank at a rate r = 100 liters/h. How long does it take for seawater in the tank to become just drinkable ?(e) Comment on what would happen if your motors were more powerful.

Answered: Image /qna-images/answer/69529b34-8f0c-44e8-b2ed-a581fee089a1.jpg

You have a shortage of drinkable water in your town and are trying to prepare safe drinking water by mixing river water with concentrated sea water. A tank initially has S0 amount of salt mixed in 1000 liters of water in it. River water enters the tank at a rate of r liters/h and the salt concentration of this water is 0.01 g/liter. Assume that the water salt mixture is well-stirred. It is also given that water is drained from the tank at the same rate as it comes in. (a) Find the differential equation which describes this scenario. You must explain in your own words and logically derive the equation. (b) Solve for S (t) in terms of r, So and t(time in hours). (c) New York's department of health recommends that salt concentration should not exceed 0.02 g/liter for the water to be drinkable. Given that, initially the sea water contains 35 g/liter liters of salt. You keep measuring the amount of salt in the tank and note that after a while it is no longer changing significantly. What is the amount of salt now ? Calculate the salt concentration and comment on whether the water in the tank is safe to drink. (d) The town provides you with industrial motors which pumps river water into the tank at a rate r = 100 liters/h. How long does it take for sea water in the tank to become just drinkable ? (e) Comment on what would happen if your motors were more powerful.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Concept explainers

Question

100%

You have a shortage of drinkable water in your town and are trying to prepare safe drinking water by mixing river water with concentrated sea water. A tank initially has S0 amount of salt mixed in 1000 liters of water in it. River water enters the tank at a rate of r liters/h and the salt concentration of this water is 0.01 g/liter. Assume that the water salt mixture is well-stirred. It is also given that water is drained from the tank at the same rate as it comes in. (a) Find the differential equation which describes this scenario. You must explain in your own words and logically derive the equation. (b) Solve for S (t) in terms of r, So and t(time in hours). (c) New York's department of health recommends that salt concentration should not exceed 0.02 g/liter for the water to be drinkable. Given that, initially the sea water contains 35 g/liter liters of salt. You keep measuring the amount of salt in the tank and note that after a while it is no longer changing significantly. What is the amount of salt now ? Calculate the salt concentration and comment on whether the water in the tank is safe to drink. (d) The town provides you with industrial motors which pumps river water into the tank at a rate r = 100 liters/h. How long does it take for sea water in the tank to become just drinkable ? (e) Comment on what would happen if your motors were more powerful.

1. You have a shortage of drinkable water in your town and are trying to prepare
safe drinking water by mixing river water with concentrated sea water. A tank
initially has So amount of salt mixed in 1000 liters of water in it. River water
enters the tank at a rate of r liters/h and the salt concentration of this water
is 0.01 g/liter. Assume that the water salt mixture is well-stirred. It is also
given that water is drained from the tank at the same rate as it comes in.
00
rliters/n
(a) Find the differential equation which describes this scenario. You must
explain in your own words and logically derive the equation.
(b) Solve for S (t) in terms of r, So and t(time in hours).
(c) New York's department of health recommends that salt concentration
should not exceed 0.02 g/liter for the water to be drinkable. Given
that, initially the sea water contains 35 g/liter liters of salt. You keep
measuring the amount of salt in the tank and note that after a while it
is no longer changing significantly. What is the amount of salt now ?
Calculate the salt concentration and comment on whether the water in
the tank is safe to drink.
(d) The town provides you with industrial motors which pumps river water
into the tank at a rate r = 100 liters/h. How long does it take for sea
water in the tank to become just drinkable ?
(e) Comment on what would happen if your motors were more powerful.

Expert Solution

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning