A tank initially contains 120 liters of water with 50 grams of salt.
The tank is rinsed with fresh water flowing in at a rate of 7 liters per minute
and leaving the tank at the same rate. The water in the tank is well-stirred.

Find the function V volume of water in the tank, in liters,

Find the differential equation satisfied by the function values Q(t),
the total amount of salt in the tank at time t, measured in grams,
Q'(t) =

Find the function Q, the amount of salt grams in the tank as function of time,

Find the time t such that the amount of salt in the tank is 30g

Question

A tank initially contains 120 liters of water with 50 grams of salt. 
The tank is rinsed with fresh water flowing in at a rate of 7 liters per minute 
and leaving the tank at the same rate. The water in the tank is well-stirred.


 Find the function V volume of water in the tank, in liters,

 Find the differential equation satisfied by the function values Q(t), 
the total amount of salt in the tank at time t, measured in grams,
Q'(t) =

 Find the function Q, the amount of salt grams in the tank as function of time,

Find the time t such that the amount of salt in the tank is 30g

anonymous · Answer

What do you mean by find V? Isn't it just a constant 120?

anonymous · Answer

At any moment we have 0 salt flowing into the tank, and 7/120 x salt flowing out, where x is the concentration in grams per litre, and the units are litres per minute.

anonymous · Answer

Thus Q'(t) = 7Q(t) / 120.