Question

A certain clock is losing time. The clock loses $\frac{2}{15}$ seconds every minute. How many seconds does the clock lose in one hour?

Answer 1

So each second we lose 2/15 of a second
There are 3600 seconds in an hour \((60~ seconds/min \times 60 ~mins/hour\)
The first second we lose 2/15, by the second second we lose the same amount, 2/15, that's \(2\times \cfrac{2}{15}\) seconds lost after 2 seconds; by the nth second we have lost \(\large n\times \left (\cfrac{2}{15}\right )\) seconds

Therefore, after one hour rather than 3600 seconds the clock shows
$$
3600-3600\times\cfrac{2}{15}=3600\times\left (1-\cfrac{2}{15}\right )=3600\times\cfrac{13}{15}~seconds
$$

Does this make sense?

Answer 2

yeah

Answer 3

great!