Answer
$200~~$ reflections would occur.
Work Step by Step
We can find the distance that the sound travels in this time:
$d = v~t = (343~m/s)(15~s) = 5145~m$
We can find the number of required reflections:
$\frac{5145~m}{25.7~m} = 200$
$200~~$ reflections would occur.
