Answer
It takes $~~2.08~hours~~$ for the water to fall a distance of $0.250~d$
Work Step by Step
Note that the amplitude is $0.50~d$
We can find the angle $\theta$ when $y = 0.250~d$:
$y = (0.50~d)~cos(\theta) = 0.250~d$
$cos(\theta) = 0.50$
$\theta = cos^{-1}~(0.50)$
$\theta = 60^{\circ}$
Note that $60^{\circ}$ is a fraction $\frac{1}{6}$ of a full cycle of $360^{\circ}$
We can find $\frac{1}{6}$ of the period:
$t = (\frac{1}{6})~(12.5~h) = 2.08~h$
It takes $~~2.08~hours~~$ for the water to fall a distance of $0.250~d$
