This is the boss. No calculator. Every number this morning is chosen to fit in your head: doses land on whole milligrams, the flow is 1 or 2 MGD, and the baffling factors are tenths. The only awkward constant is 8.34, and it splits cleanly — $6 \times 8.34 = 48 + 2.04 = 50.04$.

One shift, five lines, and every answer feeds the next: demand and residual give the dose, the dose and the flow give the pounds, the detention time and the baffling factor give the real contact time, the residual and that contact time give the CT, and the CT against the table gives the verdict. Write each line down as you go — a slip on line one walks all the way to the regulator.

Watch the two places this morning is built to catch you. The C in CT is the residual, not the dose — the water ate the difference on the way through. And the T in CT is T₁₀, not the detention time — applying the baffling factor on line three and then quietly using θ on line four is the commonest false pass in the trade, and it is the one that ends up in the newspaper.

Note what the last line actually asks for. Not another number: a decision. Does this plant earn its credit this morning, yes or no. The arithmetic exists only to earn you the right to make it — and on some of these mornings the chemistry is faultless and the plant still fails, because the water went round the outside of the basin.

Everything in the chapter rides in this one shift. 5★ under par here is the chapter crown. Clock in.