13.199. On the way from the village to the field, the truck's wheel makes 100 fewer revolutions than the bicycle's wheel and 150 more revolutions than the tractor's track. Find the distance between the village and the field, given that the circumference of the truck's wheel is $4 / 3$ of the circumference of the bicycle's wheel and 2 m shorter than the tractor's track.
## Solution.

Let $x$ m be the distance between the village and the field, $y$ m be the circumference of the bicycle wheel; $\frac{4}{3} y$ m be that of the truck, $\left(\frac{4}{3} y+2\right)$ m be that of the tractor.

The truck wheel makes $\frac{x}{\frac{4}{3} y}$ revolutions; the bicycle wheel makes $-\frac{x}{y}$ revolutions; the tractor wheel makes $-\frac{x}{\frac{4}{3} y+2}$ revolutions. According to the conditions, $\left\{\begin{array}{l}\frac{x}{\frac{4}{3} y}=\frac{x}{y}-100, \\ \frac{x}{\frac{4}{3} y}=\frac{x}{\frac{4}{3} y+2}+150,\end{array}\right.$ from which $x=600$ m.

Answer: 600 m.