3.39 $A$ and $B$ working together can complete a job in 2 days, $B$ and $C$ working together can complete it in 4 days, $C$ and $A$ working together can complete it in $2 \frac{2}{5}$ days, the number of days $A$ alone can complete the job is
(A) 1 .
(B) 3 .
(C) 6 .
(D) 12 .
(E) 2.8 .
(5th American High School Mathematics Examination, 1954)
[Solution] Let $x, y, z$ be the number of days required for $A, B, C$ to complete the work individually. We have
$$
\left\{\begin{array}{l}
\frac{1}{x}+\frac{1}{y}=\frac{1}{2}, \\
\frac{1}{y}+\frac{1}{z}=\frac{1}{4} \\
\frac{1}{z}+\frac{1}{x}=\frac{5}{12} .
\end{array}\right.
$$
(1) - (2) + (3) gives $\frac{2}{x}=\frac{2}{3}$, solving for $x$ yields $x=3$. Therefore, the answer is $(B)$.