Petr and Michal set up their tents in the campground. When Petr first goes to Michal and then to the dining hall, he walks 20 meters more than if he went directly to the dining hall. When Michal first goes to Petr and then to the dining hall, he walks 16 meters more than if he went directly to the dining hall. How many meters apart are the friends' tents? Which of them had a longer direct route to the dining hall? By how many meters?

(Dillingerová)
Let $p$ be the distance (in meters) from Peter's tent to the dining hall, $m$ the distance (in meters) from Michal's tent to the dining hall, and $s$ the distance (in meters) between the two tents. Peter's route to the dining hall via Michal's tent: $s+m$ meters, Michal's route to the dining hall via Peter's tent: $s+p$ meters. For Peter's route, we have: $s+m=p+20$, and for Michal's route: $s+p=m+16$. By adding both equations, we get: $2 s+m+p=m+p+36$, thus $s=18$ meters, which is the answer to the first question.

The answer to the second and third questions can be obtained by substituting the distance between the tents into one of the equations. We get: $18+m=p+20$, thus $m=p+2$. This means that Michal's tent is $2 \mathrm{~m}$ farther from the dining hall than Peter's.