## 146. Math Puzzle $7 / 77$

During a section of a cycling race, the peloton is rolling at $v=40 \mathrm{~km} / \mathrm{h}$. A rider loses three minutes due to a flat tire.

At what speed must he chase the peloton to catch up after $20 \mathrm{~km}$?
The cyclist must follow the field at the speed $v_{F}$. Then, for the distances covered, since he is short of $3 \mathrm{~min}=\frac{1}{20}$ time $(t=$ driving time for the $20 \mathrm{~km})$:

Cyclist: $v_{F} \cdot\left(t-\frac{1}{20}\right)=20$, from which it follows

Field: $40 \cdot t=20 ; t=0.5 \mathrm{~h} ; V_{F}=44.4 \frac{\mathrm{km}}{\mathrm{h}}$