Question

A tank initially contains 200 gallons of brine, with 50 pounds of salt in solution. brine containing 2 pounds of salt per gallon is entering the tank at the rate of 4 gallons per minute and is is flowing out at the same rate. if the mixture in the tank is kept uniform by constant stirring, find the amount of salt in the tank at the end of 40 minutes. the amount of salt in the tank at the

Answer 1

The amount of salt in the tank at the end of 40 minutes is still 50 pounds.

Step-by-step explanation:

To find the amount of salt in the tank at the end of 40 minutes, we need to calculate the change in the amount of salt in the tank over that time period.

The tank contains 200 gallons of brine with 50 pounds of salt in solution. Brine containing 2 pounds of salt per gallon is entering and exiting the tank at a rate of 4 gallons per minute.

Since the rate of flow in and out of the tank is the same, the amount of salt in the tank remains constant. Therefore, the amount of salt in the tank at the end of 40 minutes is still 50 pounds.

Answer 2

suppose you wanted the tank to hold 100 gallons of water and it was 50 gallons per cubic feet. How many cubic feet would you need? Obviously, 2 cubic feet. How did you get that?? Well, you divided 100 by 50 to get 2.

O.K., now, let's try YOUR problem. 225000 gallons and 7.5 gallons per cubic feet. How many cubic feet do you need? Must be 225,000/7.5 = 30,000 cubic feet

O.K., now we're half way there. we (should) know that the volume of a prism is

l x w x h. We now know the volume must also be 30,000

so l x w x h = 30000
100 x 20 x h = 30000

you should be able to take it from there.

Problem #2

We approach it the exact same way.

It's too hard as stated. Let's make up an easier problem.

suppose 1 gallon took up 5 cubic feet. If you had 10 cubic feet, how many gallons would you have?
well, clearly, you would have 2 gallons. How did you get it?

Now, how many cubic feet in the cylinder? Well you (should) know that the volume of a cylinder is:

Pi r^2h = 3.14 x 25^2 h = 1962.5 h

Now we have a bit of a problem. You didn't tell me how high the tank is. Let us say it is 10 feet.

So, the tank had 19,625 cubic feet.

Go back to the start of this problem and you will know what to do next.