How do I solve this tedious physics question?

Question

A spelunker (cave explorer) drops a stone from rest into a hole. The speed of sound is 343 m/s in air, and the sound of the stone striking the bottom is heard 1.36 s after the stone is dropped. How deep is the hole?

______m

Answer 1

8.69 m

Answer 2

The speed of sound is so much faster than the speed of the rock that it can be ignored (at least to a first approximation).  Then, we can use s = 0.5 g t^2 to get the distance, which turns out to be 9.0630 meters.  Dividing this by 343 meters per second give a timing error of 26 milliseconds, less than 2% of the total time.  For a detailed examination, some algebra can be done; the result will be a quadratic equation which can be solved by the usual means.