1.108 If $b$ people can lay $f$ bricks in $c$ days, then $c$ people working at the same rate can lay $b$ bricks in
(A) $f b^{2}$.
(B) $\frac{b}{f^{2}}$.
(C) $\frac{f^{2}}{b}$.
(D) $\frac{b^{2}}{f}$.
(E) $\frac{f}{b^{2}}$.
(22nd American High School Mathematics Examination, 1971)
[Solution] If $x, y, z$ represent the number of people, days, and the number of bricks respectively, and $k$ is a constant of proportionality, then $z=k x y$. From the problem, we get $k=\frac{f}{b c}$.
Then the number of days is
So the answer is $(D)$.
$$
y=\frac{b c z}{f x}=\frac{b c b}{f c}=\frac{b^{2}}{f} .
$$