A stone is dropped into a well and the report of the stone striking the bottom is heard 7.7 seconds after it is dropped. Assume that the stone falls 16** (**t squared**)** feet in t seconds and that the velocity of sound is 1,120 feet per second. The depth of the well is:

Help pls.

1. Per definition \(\displaystyle distance = speed \cdot time\).

2. The total time is split into two parts: The time t which is needed by the falling stone and the remaining time (7.7 - t) which is needed by the sound. The falling stone and the sound have to pass the same distance d:

\(\displaystyle d_{stone} = 16 \cdot t^2\)

\(\displaystyle d_{sound} = 1120 \cdot (7.7-t)\)

3. Solve for t:

\(\displaystyle 16 \cdot t^2 = 1120 \cdot (7.7-t)\)

4. Plug in the value of t into one of the equations determining d to get the depth of the well.