I do not have a pocket watch at the moment, is under repair at the clockmaker, and my wall clock stopped. So I go to a friend, where - as I know - clocks always work perfectly, I spend some time with him, and after returning home I set my clock exactly exactly. How could I have done this, if you didn't know before, how much time is needed, to go from my apartment to my friend's apartment?
The task comes down to this, to set the exact hour after I got home. Well, just before I leave the house, I wind up my clock, I set it for any hour; I denote this hour with the letter a. I immediately go to my friend and write them down as soon as I come to him, what time is on his clock; I mark this hour with the letter b.
Having chatted with a friend (.. . and after drinking black coffee) I arrange just before leaving, what time is it according to his clock; let it be c. Returning home, I find, what time my clock is on at random; let it be the hour d.
On my way home, I had a plan of action prepared, so, a minute after my return, my clock was on the correct time; it was e.
Here are the calculations:
The difference d - a indicates, how much time have I been away from home:
d — a = godz. 3 min. 50 - hours. 3 min. 00 = 50 min.
The difference c - b indicates, how much time i spent with a friend:
c — b — godz. 5 min. 46 - hours. 5 min. 12 = 34 min.
Difference (d — a) — (c — b) points, how much time did I go from my house to my friend and back:
(d — a) — (c — b) = 50 min. — 34 min. = 16 min.
I tried to walk in both directions steadily, so I can accept, that I used half the time on the way back:
[(d – a) — (c — b)] / 2 = 8 min.
Adding this half to the c hour will give me the exact hour when I return home:
at. 5 min. 46 + 8 min. = 5 at. 54 min.
I added one more minute wasted on calculations - and here's a good time!