## 13. Math Puzzle $6 / 66$

A stenotypist has a long manuscript to transcribe. For the first half, she types 15 pages per day, and for the second half, she types 25 pages per day.

What is her average daily output overall?
If the manuscript has $2 M$ pages, she needs $\frac{M}{15}$ days for the first half, $\frac{M}{25}$ days for the second half, and in total for $2 M$ pages:

$$
\frac{M}{15}+\frac{M}{25}=\frac{8}{75} M \text { days }
$$

Thus, she writes on average $\frac{2 M}{\frac{8}{75} M}=\frac{75}{4}=18.75$ pages per day.