From the road

Dear all, I am writing from the third day of the journey. We left at dawn on Monday and have covered about four hundred and fifty kilometres so far, a hundred and fifty a day.

Dear all: day $3$ of the journey. Left Monday at dawn; $\approx 450$ km so far $=150$ km a day.

all: $t=3$ d. $x(3)\approx 450$ km, $\bar{v}=150$ km/d.

The road climbs. We began at sea level and tonight we sleep at eighteen hundred metres; it is about twelve degrees colder up here than where we started.

The road climbs: from $0$ m to $1800$ m tonight; $\approx 12^{\circ }$ colder than at the start (about $6.5^{\circ }$ per $1000$ m).

$h:0\to 1800$ m. $\Delta T\approx -6.5^{\circ }\cdot 1.8\approx -12^{\circ }$ ($6.5^{\circ }$ per km up).

Of the twelve of us, two are already homesick, nine are happy, and one is asleep and cannot be counted either way.

Of the $12$ of us: $2$ homesick, $9$ happy, $1$ asleep, $2+9+1=12$.

$|U|=12$: $2$ homesick $+9$ happy $+1$ asleep.

If the pace holds, we reach the lake on the sixth day, rest for two, and are home on the fourteenth. I have spent a third of my coins and only three days of fourteen have passed; at this rate they last nine days, not fourteen, which worries me a little.

If the pace holds: lake on day $6$, rest $2$ days, home on day $14$. Coins: $\frac{1}{3}$ spent in $3$ days of $14$; at this rate they last $3\times 3=9$ days $<14$, which worries me a little.

pace $\Rightarrow$ lake$(6)$, rest$[7,8]$, home$(14)$. $c(3)=\frac{2}{3}{c}_0\Rightarrow c(9)=0$, $9<14$ (!)

Do not worry about me: the days are long, the bread is cheap, and the mountains are bigger than any trouble I have brought with me. Write to the inn at the lake today; a letter takes four days, so it will arrive on the seventh day, while I am still resting there.

Don't worry: days long, bread cheap, mountains $\gg$ any trouble I brought. Write to the inn at the lake today: a letter takes $4$ days $\Rightarrow$ it arrives on day $3+4=7$, while I am still resting there.

worry $=0$: day long, bread cheap, mountain $\gg$ trouble. write$(3)\to$ inn$(3+4=7)$; me $\in$ inn for $t\in [6,8]$ ✓.