Problem

Source: 2021 Dürer Math Competition Regional E1 https://artofproblemsolving.com/community/c2773609_2021_

Tags: number theory



Albrecht is travelling in his car on the motorway at a constant speed. The journey is very long so Marvin who is sitting next to Albrecht gets bored and decides to calculate the speed of the car. He was a bit careless but he noted that at noon they passed milestone $XY$ (where $X$ and $Y$ are digits), at $12:42$ milestone $YX$ and at $1$pm they arrived at milestone $X0Y$. What did Marvin deduce, what is the speed of the car?