A doubt in modelization of a problem related to differential equations

[dunkelheit]

I was trying to modelize this problem

A tank contains 50 liters of a liquid [MATH]L_1[/MATH] and 50 liters of a liquid [MATH]L_2[/MATH]. In the tank is inserted a liquid [MATH]L_2[/MATH] with a flow rate of 5 liters per minute. At the same flow rate the solution of [MATH]L_1[/MATH] and [MATH]L_2[/MATH] is taken out. How much liquid [MATH]L_1[/MATH] will be in the tank after one hour?

The idea is trying to find how the percentage of liquid [MATH]L_1[/MATH] varies with respect to time: because the conservation of mass implies the conservation of volumes, we have that the problem can be described by the equation "volume of liquid [MATH]L_1[/MATH] at a certain instant of time equals volume of liquid [MATH]L_1[/MATH] in a former instant of time minus volume of liquid [MATH]L_1[/MATH] taken out in the interval of time between the two instants".
We don't know the last term of the equation, but if we suppose that the interval of time is very small we can suppose that hte percentage of liquid [MATH]L_1[/MATH] doesn't change; so if we call [MATH]f_i(t)[/MATH] the liters of liquid [MATH]L_i[/MATH] in the tank, [MATH]t_0[/MATH] the initial time of the process and [MATH]\Delta t[/MATH] the interval between two times we get to the approximated relation

[MATH]f_1(t_0+\Delta t) \ \text{liters}=f_1(t_0) \ \text{liters}-\Delta t \frac{f_1(t_0) \ \text{liters}}{f_1(t_0) \ \text{liters}+f_2(t_0) \ \text{liters}} \cdot 5 \frac{\text{liters}}{\text{min}}[/MATH]​

The doubt is the following: I understand that the quantity [MATH]\Delta t \cdot 5 \frac{\text{liters}}{\text{min}}[/MATH] is the flow rate in [MATH]\Delta t[/MATH] because it is simply the flow rate multiplied by how much time is passed, but I don't get why the coefficient [MATH]\frac{f_1(t_0) \ \text{liters}}{f_1(t_0) \ \text{liters}+f_2(t_0) \ \text{liters}}[/MATH] rapresent the fact that the solution of [MATH]L_1[/MATH] and [MATH]L_2[/MATH] is exiting and the liquid [MATH]L_1[/MATH] is entering.
In poor words: why the matematical operation of ratio between [MATH]f_1(t_0)[/MATH] and [MATH]f_1(t_0)+f_2(t_0)[/MATH] modelize correctly the action of inserting the liquid [MATH]L_1[/MATH] and extracting the solution of [MATH]L_1[/MATH] and [MATH]L_2[/MATH] from the tank?
Thanks.