One method for determining the depth of a well is to drop a stone into it and then measure the time it takes until the splash is heard. If d is the depth of the well (in feet) and t1 the time (in seconds) it takes for the stone to fall, then d = 16t12, so t1 = √d/4.
Now if t2 is the time it takes for the sound to travel back up, then d = 1090t2 because the speed of sound is 1090 ft/s. So t2 = d/1090. Thus, the total time elapsed between dropping the stone and hearing the splash is given by the following equation.
t1 + t2 = √d/4 + d/1090
How deep is the well if this total time is 3.1 s? (Round the answer to the nearest whole number.)