Answer
The length of the rod is $~~44~m$
Work Step by Step
Let $L$ be the length of the rod.
We can find an expression for the time it took the sound to travel through the rod:
$t_r = \frac{L}{15v}$
We can find an expression for the time it took the sound to travel through the air:
$t_a = \frac{L}{v}$
Note that: $~~t_a = t_r+0.12~s$
We can use $t_a$ to find another expression for the time $t_r$:
$t_a = \frac{L}{v} = t_r+0.12$
$t_r = \frac{L}{v} - 0.12~s$
We can find $L$:
$\frac{L}{15v} = \frac{L}{v} - 0.12$
$L = 15~L - (0.12)(15~v)$
$14~L = (0.12)(15~v)$
$L = \frac{(0.12)(15~v)}{14}$
$L = \frac{(0.12~s)(15)(343~m/s)}{14}$
$L = 44~m$
The length of the rod is $~~44~m$
