As part of a fabrication process, you encounter the following scenario. A vat contains 100 liters of water. In error someone pours 100 grams of a chemical into the vat instead of the correct amount, which is 50 grams. To correct this condition, a stopper is removed from the bottom of the vat allowing 1 liter of the mixture to flow out each minute. At the same time, 1 liter of fresh water per minute is pumped into the vat and the mixture is kept uniform by constant stirring.
Show that if x(t) represents the number of grams of chemical in the solution time t, the equation governing x is

dx/dt= -x/100

where x(0) =100. How long will it take for the mixture to contain the desired amount of chemical?