Tank Mixing Problem - Just for Fun if you'd like to spend time on it

[rbzima]

Hey, here's a fun problem many of you would probably enjoy trying. I've done it myself, and it truly is a fun problem to do. Here it is:

We have an initial amount of 800 gallons in a tank at 8:00 in the morning on any particular day. 35% of that 800 gallon solution is acidic. Spigot A is turned on every morning at 8:00 AM, putting 15% acidic solution into the tank. 8:30 AM is when Spigot B at the bottom of the tank is turned on, which drains the tank for customer use.

Both spigots range in the rate at which the liquid is coming in and out of the tank. This range is between 4.0 and 4.5 gallons per minute. Everyday I go to ACME ACID to fill my 40 gallon container at 9:00 AM, and I would like the company to guarantee the range of acidity level in my container.

Therefore, we are looking for the narrowest range of acidity when the 40 gallon container is filled completely.

Secondly, if the attendant at ACME ACID one day measures the tank at 8:20 and discovers there to be 884 gallons in the tank, we are looking for the narrowest range of acidity in the 40 gallon container with this taken into account.

Go Nuts!

 

[Gza]

Hey, here's a fun problem many of you would probably enjoy trying. I've done it myself, and it truly is a fun problem to do. Here it is:

We have an initial amount of 800 gallons in a tank at 8:00 in the morning on any particular day. 35% of that 800 gallon solution is acidic. Spigot A is turned on every morning at 8:00 AM, putting 15% acidic solution into the tank. 8:30 AM is when Spigot B at the bottom of the tank is turned on, which drains the tank for customer use.

Both spigots range in the rate at which the liquid is coming in and out of the tank. This range is between 4.0 and 4.5 gallons per minute. Everyday I go to ACME ACID to fill my 40 gallon container at 9:00 AM, and I would like the company to guarantee the range of acidity level in my container.

Therefore, we are looking for the narrowest range of acidity when the 40 gallon container is filled completely.

Secondly, if the attendant at ACME ACID one day measures the tank at 8:20 and discovers there to be 884 gallons in the tank, we are looking for the narrowest range of acidity in the 40 gallon container with this taken into account.

Go Nuts!

You really have to give the posters at this forum a little more credit than that

Come on, we both know this problem probably isn't very fun for most people who know how to do it, and this is obviously a homework problem, so why don't you go ahead and show some work and where you're stuck if you want assistance.

edit: actually you'd probably be better off putting this in the homework help section

 

[rbzima]

Actually, I did it last semester and already know the answer, because it was a coursework project. If you'd like, I can send you the entire project right now from last semester. I thought people here might like to try something challenging.

Just a reiteration: THIS IS NOT HOMEWORK OR ANYTHING RELATED TO COURSEWORK DUE THIS SEMESTER. If I knew how to upload the whole thing, I would do so, but it's sad I don't.