tank problem Differential equation A tank is partially filled with 100 gallons of coffee in which 10 lbs of sugar is dissolved. Coffee containing 1/3 lb of sugar per gallon is pumped into the tank at rate 3 gal/min. The yummy well-mixed solution is then pumped out at a slower rate of 1 gal/min. 
A- What is the rate at which the tank is increasing before the tank is full? 
B- Set up a differential equation for finding the number of pounds A(t) of sugar in the tank at anytime? 
for part A i'm not sure but for part B i think that it should be something like that 
dA(t)/t= (1/3)(3)-(A(t)/100)(3) but I'm not sure how to finish this 

So you have $dA/dt = (\text{A in}) - (\text{A out})$. For $\text{A in}$, you want to find the concentration of the input (lbs/gal) and multiply it by the volume input (gal/min) to get the A input (lbs/min). You did this correctly. 
For $\text{A out}$ you want to do the same. Find the concentration of the output (lbs/gal) and multiply it by the volume output (gal/min) to get the A output (lbs/min). Your volume output is 1 gal/min. Your output concentration is A(t)/V(t), where V(t) is the current volume of the tank. In a simpler problem, this volume would be constant, but here it isn't, because the input and output flow rates are different. What is it here?
