**Time and Work — formulas used here.** - Work done in unit time. If a…

Question

**Time and Work — formulas used here.**

- Work done in unit time. If a worker finishes a job in $m$ days, the fraction of work done in one day is $	frac{1}{m}$.
- Combined work (two workers). A finishes in $X$ days, B in $Y$ days; together they finish in $	frac{XY}{X+Y}$ days.
- Combined work (three workers). A, B, C take $X$, $Y$, $Z$ days; together they take $	frac{XYZ}{XY+YZ+ZX}$ days.
- Efficiency–time inverse. If A is $k$ times as efficient as B, A takes $	frac{1}{k}$ as long.
- Workforce equivalence. $M_1 D_1 T_1 = M_2 D_2 T_2$ for the same work, where $M$ = workers, $D$ = days, $T$ = hours/day.

**Question.** If A can finish a piece of work in 12 days, what fraction of the work does A finish in a single day?

Accepted Answer

C. $\dfrac{1}{12}$

Directly applying the unit-rate rule: if a worker finishes a job in $m$ days, one day's work is $	frac{1}{m}$. For $m = 12$, that is $	frac{1}{12}$.

Answer

$\dfrac{1}{6}$

Answer

$\dfrac{1}{8}$

Answer

$\dfrac{1}{24}$