3.33 A person walks a certain distance at a uniform rate. If he walks $\frac{1}{2}$ mile per hour faster, he will take only four-fifths of his original time; if he walks $\frac{1}{2}$ mile per hour slower, he will take $2 \frac{1}{2}$ hours more. The number of miles in the distance he walks is
(A) $13 \frac{1}{2}$.
(B) 15 .
(C) $17 \frac{1}{2}$.
(D) 20 .
(E) 25 .
(23rd American High School Mathematics Examination, 1972)
［Solution］Let $D, R, T$ represent distance (miles), rate (miles/hour), and time (hours), respectively. Then, by the given conditions, we have
$$
D=R T,
$$

and $D=\frac{4}{5}\left(R+\frac{1}{2}\right) T$,
and $D=\left(R-\frac{1}{2}\right)\left(T+2 \frac{1}{2}\right)$.
From equations (1) and (2), we get $\frac{1}{5} D=\frac{2}{5} T$, which simplifies to $D=2 T$.
Thus, $\quad 2 T=R T, \quad R=2$.
Substituting $\frac{1}{2} D$ for $T$ and 2 for $R$ into equation (2), we get $D=\frac{3}{2}\left(\frac{1}{2} D+2 \frac{1}{2}\right)$, $\therefore \quad D=15$.
Therefore, the correct choice is $(B)$.