# Math Help - Connected tanks.

1. ## Connected tanks.

I have had this problem for a week now. I do not even know where to begin.

You have 26 tanks of water.
1 giant tank that holds a maximum of 27million L
25 smaller tanks that hold a maximum of 130k L each
You have 5 pumps that are filling the 25 smaller tanks with 10k L per second divided evenly among all the smaller tanks (each pump does 10k L/s)(this water comes from nowhere, infinite amount)
You have 17 pumps that are pumping water out of the large tank at a rate of 10k L per second (this water goes nowhere)
The giant tank is also pumping 30% of the current amount of water from each of the smaller tanks to itself every 1 second.
The giant tank starts at 14mil L
The Smaller tanks start at 130k L each

At what rate would the Giant tank become empty?

I know that the large tank is draining at a rate of 170,000 liters per second
I know that the smaller tanks are filling at a rate of 2,000 liters per second each
What I cant figure out is the rate at which the Large tank is filling, or the rate at which the smaller tanks are draining.

2. y = 1400 + [((5*130)+50*x)- (((5*130)+50*x)*.30)] - (170*x)
This is the closest I can get, which shows the tank draining at 1855 seconds after starting
Although, my formula doesn't seem anywhere near complicated enough to account for the 30% per second.

3. Originally Posted by mpweber
I have had this problem for a week now. I do not even know where to begin.

You have 26 tanks of water.
1 giant tank that holds a maximum of 27million L
25 smaller tanks that hold a maximum of 130k L each
You have 5 pumps that are filling the 25 smaller tanks with 10k L per second divided evenly among all the smaller tanks (each pump does 10k L/s)(this water comes from nowhere, infinite amount)
You have 17 pumps that are pumping water out of the large tank at a rate of 10k L per second (this water goes nowhere)
The giant tank is also pumping 30% of the current amount of water from each of the smaller tanks to itself every 1 second.
The giant tank starts at 14mil L
The Smaller tanks start at 130k L each

At what rate would the Giant tank become empty?

I know that the large tank is draining at a rate of 170,000 liters per second
I know that the smaller tanks are filling at a rate of 2,000 liters per second each
What I cant figure out is the rate at which the Large tank is filling, or the rate at which the smaller tanks are draining.
If I interpreted your post correctly ...

let $V$ = volume in kL of the large tank at any time t in seconds

$y$ = total volume of all the smaller tanks at any time t in seconds

$\dfrac{dy}{dt} = 50 - 0.3y$

$y(0) = 3250 \, kL$

solving this DE for $y$ ...

$y = \dfrac{10}{3}(50 + 925e^{-0.3t})$

$\dfrac{dV}{dt} = 0.3y - 170$

$\dfrac{dV}{dt} = -120 + 925e^{-0.3t}$