A30-gallon tank initially contains 15 gallons of salt water containing 6 pounds of salt. suppose salt water containing 1 pound of salt per gallon is pumped into the top of the tank at the rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. how much salt is in the tank when the tank is full

 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.

The slope of the function is 0.5.