Differential Equation Water Tank Word Problem

[aves]

I am having trouble starting this problem:

A tank is filled with 1000 liters of pure water. Brine containing 0.08 kg of salt per liter enters the tank at 9 liters per minute. Another brine solution containing 0.03 kg of salt per liter enters the tank at 9 liters per minute. The contents of the tank are kept thoroughly mixed and the drains from the tank at 18 liters per minute.

A. Determine the differential equation which describes this system. Let S(t) denote the number of kg of salt in the tank after t minutes. Then:
dS/dt=?

Any help on how to start this would be appreciated

 

[tiny-tim]

welcome to pf!

hi aves! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[aves]

I am not even sure how to make the differential equation out of the word problem. I can do the rest from there, but I just can't figure it out.

 

[Ray Vickson]

Hint: in a small interval of time [itex] \Delta t > 0, [/itex] how many kg of salt enters the tank? How many kg of salt leaves the tank?

RGV

 

[tiny-tim]

I am not even sure how to make the differential equation out of the word problem. I can do the rest from there, but I just can't figure it out.

ok, let's start with the letters …

the question helps you on this, telling you to use "t" for time, in seconds, and S for the total weight of salt, in kg

now try translating into an equation the effect of …

Brine containing 0.08 kg of salt per liter enters the tank at 9 liters per minute.

 

[aves]

Would it follow the general equation: S(t)=S0*e^(kt)?
Where t is the time and S0 is the initial weight of salt (0.08 kg)?

 

[tiny-tim]

don't solve it

just write it!

dS/dt = … ? ​

 

[aves]

Would it be:
dS/dt=0.72+0.27-18S/1000
?