Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose a tank with a total capacity of 60 Gallons is currently only half full of a solution of water with 2% bleach concentration. At time t=0 water with a bleach concentration of 7% is pumped in at a rate of 2 gallons per minute. Water is drained from the tank at a rate of 1 gallon per minute. When the tank is full, everything shuts off. What is the amount of bleach in the tank at this time, and what is the concentration?

I don't need it worked out I just want to know if I set this up right. let me know what i need to add or change anything.

dA/dt = (2)(.07)-(1)(A/30+t)

share|cite|improve this question
Looks good to me. If you have to solve it then you will need to write down an initial condition too. – David Feb 5 '14 at 5:58
yeah in this case that would be A(0)=.6 right? – joe Feb 5 '14 at 6:00
Yes, that's right. – David Feb 5 '14 at 6:01
Now when I solve for t when the tank is 60 gallons i get 827.89 mins which seems to much for me i would think it takes 30 mins to fill up the rest of the tank. 2 gallons/min (pumped in) and 1 gallon/min (pumped out) which means getting 1 gallon/min so 30 mins – joe Feb 5 '14 at 6:04
Not sure what you mean "solve for $t$", the time taken is $30$ minutes, exactly as you said in the middle of your comment. And the question asks you to find $A$ when the tank is full, not $t$. – David Feb 5 '14 at 6:22

How much bleach is lost in dt?


Where C is the current amount of bleach and V is the current volume.

How much bleach is added in dt?



dC/dt = 0.07*2-C/V

And V = 30+t

Describes the amount of bleach in the tank, with the appropriate initial conditions

And you just need it at the time when the tank is full.

eta: I guess your answer is right up to missing parentheses

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.