Tokarev S.i.

A freight train, departing from Moscow at $x$ hours $y$ minutes, arrived in Saratov at $y$ hours $z$ minutes. The travel time was $z$ hours $x$ minutes.

Find all possible values of $x$.
Note that $x+y<24+24<60$, so the number of minutes of the arrival time $z=x+y$. The number of hours $y$ of the arrival time differs from the sum

$x+z=2 x+y$ by a multiple of 24 (the number of hours in a day). From this, it is clear that $x$ is a multiple of 12, and since $x<24$, either $x=0$ or $x=12$. Both values are possible: for example, the train departs at 0.15, is en route for 15 hours, and arrives at 15.15, or departs at 12.15, is en route for 27 hours 12 minutes, and arrives at 15.27.

## Answer

0 or 12.