A 100 gallon tank is filled with pure water. Water which has a concentration of 7g of salt per gallon flows into the tank at a rate of 10 gallons/min, and the mixture is stirred to a uniform concentration. Water also leaks from the tank at the same rate, 10 gallons/min.
Find a differential equation describing the rate of change of salt in the tank.
Hint: The concentration of salt in the tank is S(t)/100, where S(t) is the total amount of salt in the tank at time t, in grams. S′(t), the rate of change of salt in the tank over time, is equal to the [rate in] − [rate out].
My soultion was
$dS/dt = 7/10 − S(t)/10$ But that is incorrect. Can someone show me their workings to the solution so I know where I went wrong?
My workings were (10 gallons/mins)(7g/ gallons)-(10 gallons/mins)(s(t)/60)