1. ## related rates problem

Hi, can you explain how i might solve this problem?

A tank initially holds 100 litres of water. A sugar solution containing 0.2 kg per litre is being run into the tank at 3 litres per minute. The liquid in the tank is being continuously stirred and, at the same time, liquid from the tank is being pumped out at 2 litres per minute. If there are $m$ kg of sugar dissolved in the solution after $t$ minutes, then $\frac{dm}{dt}$ is equal to:

$\frac{3}{5} - \frac{2m}{100+t}$

But i dont know how they got it.

2. Originally Posted by scorpion007
Hi, can you explain how i might solve this problem?

A tank initially holds 100 litres of water. A sugar solution containing 0.2 kg per litre is being run into the tank at 3 litres per minute. The liquid in the tank is being continuously stirred and, at the same time, liquid from the tank is being pumped out at 2 litres per minute. If there are $m$ kg of sugar dissolved in the solution after $t$ minutes, then $\frac{dm}{dt}$ is equal to:

$\frac{3}{5} - \frac{2m}{100+t}$

But i dont know how they got it.
The volume of liquid in the tank at time $t$ is:

$v(t)=100+3t-2t=100+t$

then:

$
\frac{d}{dt}m=3\times 0.2 - \frac{2m}{v}
$

where the first term on the RHS is the rate that sugar is flowing into the tank,
and the second term is the rate at which it is flowing out of the tank.

The outflow is two litres per minute with a concentration of $m/v$ kg/litre.

RonL

3. Thank you very much. I think i understand it now.