Answer:
178 ft
let t1 = drop time, let t2 = time for sound to travel up to you, Y = well depth
t1 + t2 = 3.5
Y = 1087 t2 = 16 t1^2
Substitute: t2 = 3.5 - t1
16 t1^2 = 1087 (3.5 - t1)
16 t1^2 = 3804.5 - 1087 t1
16 t1^2 + 1087 t1 - 3804.5 = 0
Solve via quadratic equation: t1 = 3.336 s, t2 = 0.164 s
Y = 178 ft