Activated sludge is farming. There is a crop of bacteria in the basin, sewage is the feed, and the operator's job is to keep the herd the right size for the meal. Two numbers describe that, and they are two views of the same balance.

The food-to-microorganism ratio is $\dfrac{F}{M} = \dfrac{Q\,S_0}{V\,X}$ — F over M equals Q S-nought over V X. $Q$ is the influent flow in m³/d and $S_0$ — S-nought — is the influent BOD in mg/L, so $Q S_0$ is the food arriving per day. $V$ is the aeration basin volume in m³ and $X$ is the MLSS in mg/L, so $V X$ is the mass of biomass standing in the tank. Food over bugs, and the concentrations cancel each other, so the answer comes out per day: kilograms of BOD per kilogram of MLSS per day. Conventional aeration runs 0.2 to 0.5; extended aeration runs 0.05 to 0.15 and is deliberately starved.

The sludge age, or solids retention time, is $\text{SRT} = \dfrac{V\,X}{Q_w\,X_w}$. The numerator is the same inventory. $Q_w$ is the waste sludge flow in m³/d and $X_w$ its concentration in mg/L — subscript w is always the WASTE stream, drawn thick off the clarifier floor, and it is never the same as $X$. Inventory over what leaves each day gives days: how long the average bacterium lives in the plant before it is thrown away. Conventional plants hold 5 to 15 days; nitrifying plants need 10 to 20, because nitrifiers grow slowly and a young sludge washes them out before they establish.

Now the part worth carrying onto a shift. F/M and sludge age move together and oppositely: waste less sludge, the inventory grows, the sludge ages and the F/M falls. Waste more and the reverse. The operator has essentially one dial — the wasting rate — and these two numbers are the two gauges it moves.

And note which term the operator can actually change. $Q$ and $S_0$ arrive from the town and nobody negotiates with them. $V$ is concrete. Only $X$ is yours, and it moves slowly — building MLSS takes days, because you are growing it. Which is why an overloaded basin is corrected the week before the load arrives, not the afternoon after.