Problem on waste water mass balance

Question

Assignment:

BOD: Biochemical Oxygen Demand
BOD₅  is the total amount of oxygen consumed by microorganisms during the first five days of biodegradation

BOD₅ = (DO_i – Do_f)/(P)    this is the five-day BOD of a diluted sample
Where DO_i = the initial dissolved oxygen (DO) of the diluted wastewater
            DO_f = the final DO of the diluted wastewater, 5 days later
            P      = the dilution fraction =   (volume of wastewater)/(volume of wastewater plus dilution water)
A standard BOD bottle holds 300 mL, so P is just the volume of wastewater divided by 300 mL

Problem: Consider a lake with 100 X 10^6 m^2 of surface area for which the only source of phosphorus is the effluent from a wastewater treatment plant. The effluent flow rate is 0.4 m^3/s and its phosphorus concentration is 10.0 mg/L (10.0 g/m^3). The lake is also fed by a stream having 20 m^3/s of flow with no phosphorus. If the phosphorus settling rate is estimated to be 10 m/yr, estimate the average phosphorus concentration in the lake. What level of phosphorus removal at the treatment plant would be required to keep the average lake concentration below 0.010 mg/L? 

Provide complete and step by step solution for the question and show calculations and use formulas.