Put it away now

Every day I leave about six things lying around: a cup, a sock, a book, a pen and so on. Putting one thing away takes me fifteen seconds.

Each day I leave $6$ things around. Putting one away takes $15$ s.

Things per day $n$, cost of putting away now $c$ (seconds): $n=6,c=15$.

If I put each thing away at once, six things cost me ninety seconds a day, only a minute and a half. After a week I have spent ten and a half minutes in total.

At once: $6\times 15=90$ s a day. Over $7$ days: $7\times 90=630$ s, which is $630÷60=10.5$ min.

$7\times n\times c=7\times 6\times 15=630$, so $\frac{630}{60}=10.5$ min.

If I leave them, a pile grows. After a week there are forty-two things, and with a pile every thing takes twice as long, because I have to search for its place: thirty seconds each. That makes twenty-one minutes.

Left in a pile: after $7$ days there are $7\times 6=42$ things. Each now takes $2\times 15=30$ s, so $42\times 30=1260$ s, which is $1260÷60=21$ min.

Pile: $7n=42$ things at cost $2c$; $42\times 30=1260$, so $\frac{1260}{60}=21$ min.

So the pile costs double, ten and a half minutes more. The lesson is small and easy to remember: a thing put away now costs fifteen seconds, a thing put away later costs thirty.

Waiting doubles the price: $21=2\times 10.5$ min. Now costs $15$ s, later costs $30$ s.

Later costs $2c$, so $21=2\times 10.5$.