If I understood well... if there is a certain amount flowing in, there should be the same amount flowing out.
For the concentration now. Both will mix to give some concentration C, in a volume V (which you got as the exiting flow rate).
Concentration times volume gives you mass. And the rate on inflow of mass should be the same as the rate of outflow of mass.
Hence,
C1V1 + C2V2 = CV
Divide by units of time,
C1F1 + C2F2 = CF
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