23. In Linda's four-day trip, she has to walk the same distance every day. On the first day, she spent one hour walking. It is known that she spends an integer number of minutes per mile, and after that, due to fatigue, her speed decreases each day, spending 5 more minutes per mile than the previous day, and the total distance she walks is also an integer. Then, in these four days, Linda walked ( ) miles.
(A) 10
(B) 15
(C) 25
(D) 50
(E) 82
23. C.

Let Linda use $x\left(x \in \mathbf{Z}_{+}\right)$ minutes per mile on the first day. Then the distance walked on the first day is $\frac{60}{x}$, the distance walked on the second day is $\frac{60}{x+5}$, the distance walked on the third day is $\frac{60}{x+10}$, and the distance walked on the fourth day is $\frac{60}{x+15}$.
Thus, the total distance is
$$
\frac{60}{x}+\frac{60}{x+5}+\frac{60}{x+10}+\frac{60}{x+15} \text {. }
$$

Notice that the divisors of 60 are
$$
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 \text {. }
$$

Therefore, when $x=5$, the total distance is an integer. At this time,
$$
\frac{60}{5}+\frac{60}{10}+\frac{60}{15}+\frac{60}{20}=25 \text {. }
$$