13.383 Several workers complete a job in 14 days. If there were 4 more people and each worked 1 hour longer per day, then the same job would be done in 10 days. If there were still 6 more people and each worked 1 hour longer per day, then this
job would be completed in 7 days. How many workers were there and how many hours per day did they work?
Solution. Let $x$ be the number of workers, $y$ be the duration (in hours) of the workday, and $t$ be the productivity of one worker per hour. Then

$$
\begin{aligned}
& 14 x y t=10(x+4)(y+1) t=7(x+10)(y+2) t \Leftrightarrow \text { (the volume of work remains constant) } \\
& \left\{\begin{array} { l } 
{ 1 4 x y = 1 0 ( x + 4 ) ( y + 1 ) , } \\
{ 1 4 x y = 7 ( x + 1 0 ) ( y + 2 ) }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
2 x y=5 x+20 y+20, \\
x y=2 x+10 y+20 .
\end{array}\right.\right.
\end{aligned}
$$

Multiplying the second equation by 2 and then subtracting it from the first, we get $x=20$.

Answer: 20 people, 6 hours.