The slow clock

The clock in our kitchen loses four minutes every day. On Sunday I set it exactly right.

Our kitchen clock loses $4$ min a day. On Sunday I set it right.

Slowness $s$ (minutes) after $d$ days: $s(d)=4d$.

After six days, on Saturday, it was twenty-four minutes slow. It said seven thirty-six when the true time was eight o'clock, and I was almost late.

After $d=6$ days it is $4\times 6=24$ min slow: it said $7:36$ when it was $8:00$, and I was nearly late.

For $d=6$ we get $s(6)=24$: the clock says $7:36$, the true time is $8:00$.

I wondered: when will the clock be right again by itself? It would have to lose a whole twelve hours, because only then do the hands point to the same place. Twelve hours is seven hundred and twenty minutes, and seven hundred and twenty divided by four is a hundred and eighty days.

When is it right again? Only when it is $12$ h slow: $12\times 60=720$ min, and $720÷4=180$ days.

Right again: $s(d)=720⟺d=\frac{720}{4}=180$.

So the slow clock is right once in a hundred and eighty days. A stopped clock is right twice a day, which is three hundred and sixty times in the same hundred and eighty days, against once. I set my clock again anyway.

A slow clock is right once in $180$ days. A stopped clock is right $2$ times a day, so $2\times 180=360$ times in the same time, against $1$.

Slow: $1$ time. Stopped: $2\times 180=360$ times (in $180$ days).