Chapter 1.5, Problem 137E

Depth of a Well 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 $d=16t_1^2$, so $t_1=\sqrt{d}/4$. 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

$t_1+t_2=\frac{\sqrt{d}}{4}+\frac{d}{1090}$

How deep is the well if this total time is 3 s?