**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.** A is twice as efficient as B and finishes a task $30$ days earlier than B does alone. In how many days does A finish the task working alone?

Accepted Answer

C. $30$

Let B take $x$ days. A is twice as efficient, so A takes $	frac{x}{2}$ days. Given $x - 	frac{x}{2} = 30$, $	frac{x}{2} = 30$, so $x = 60$ days for B and $30$ days for A. A common trap (option D, 60) is to report B's time instead of A's.

Answer

$15$

Answer

$20$

Answer

$60$