A body takes $1 \frac{1}{3}$ times as much time to slide down a rough inclined plane as it takes to slide down an indentical but smooth inclined plane. If the angle of inclined plane is $45^{\circ}$, the coefficient of friction is:

Question

( A ) $\frac{9}{16}$
( B ) $\frac{7}{16}$
( C ) $\frac{3}{4}$
( D ) $\frac{7}{9}$