Answer
12,000 years
Work Step by Step
We treat the earth as a solid sphere. We know that there are 86,400 seconds in a day. Thus, the earth is rotating and $ 7.272205\times10^{-5} $ radians per second. If the day were a second less, the earth would rotate at $7.272289\times10^{-5}$ radians per second. Thus, we find:
$\Delta K = \frac{1}{2}(\frac{2}{5}M_ER_E^2)(( 7.272121\times10^{-5})^2-(7.272289\times10^{-5})^2)=2.97\times10^{24}$
Dividing this by $16\times10^{12}W$ and then converting to seconds, we find:
$\Delta t \approx 12,000\ years$
