Matekváros and Fizikaváros are located in different time zones. A flight departs from Fizikaváros at 8 AM local time and arrives in Matekváros the same day at noon local time. The flight departs again two hours after arrival and arrives back in Fizikaváros at 8 PM local time. The travel time is the same in both directions. What is the time in Fizikaváros when it is noon in Matekváros?
Solution. Let the plane take $x$ hours to travel the distance between the two cities, and let the time difference be $y$ hours. Based on the outbound journey, $x+y=4$, and based on the return journey, $x-y=6$. From this, $2x=10, x=5, y=-1$.

The time difference is therefore 1 hour, in favor of Mathville, because otherwise, the plane that departed at 2 PM on the return trip would have arrived at 7 PM, but upon arrival, it was already 8 PM.

Accordingly, when it is noon (12 PM) in Mathville, it is already 1 PM in Physicsville.