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 identical but smooth inclined plane. If the angle of inclination is 45°, find the coefficient of friction.

• A

  $\frac{1}{16}$

• B

  $\frac{3}{16}$

• C

  $\frac{5}{16}$

• D

  $\frac{7}{16}$