Answer:
The depth of the well, s = 54.66 m
Given:
time, t = 3.5 s
speed of sound in air, v = 343 m/s
Solution:
By using second equation of motion for the distance traveled by the stone when dropped into a well:

Since, the stone is dropped, its initial velocity, u = 0 m/s
and acceleration is due to gravity only, the above eqn can be written as:

 (1)
                     (1)
Now, when the sound inside the well travels back, the distance covered,s is given by:

 (2)
                                              (2)
Now, total time taken by the sound to travel:
t = t' + t'' 
t'' = 3.5 - t'                                                                        (3)
Using eqn (2) and (3):
s = 343(3.5 - t')                                                                 (4)
from eqn (1) and (4):
 
 
 
 
Solving the above quadratic eqn:
t' = 3.34 s 
Now, substituting t' = 3.34 s in eqn (2)
s = 54.66 m