SOLUTION: 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

Question 122451This question is from textbook College Algebra
: 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.)
Thank you for your expertise! This question is from textbook College Algebra

Answer by ddreamfox(6) (Show Source): You can put this solution on YOUR website!
Answer:
t1 + t2 = (sqrt d)/4 + d/1090 ---> Equation
Since total time is t1+t2, then t1+t2 = 3.1 secs (given)
Substituting the value to the above equation, we get:
3.1 = (sqrt d)/4 + d/1090
*multiply whole eqtn by 1090 (to eliminate denominator)
--> 3379 = 272.5(sqrt d) + d
*transpose d (from right side of equation) to the left side making it negative
--> 3379 - d = 272.5(sqrt d)
*squre both sides and simplify
--> (3379 - d)2 = (272.5(sqrt d))2
--> 11417641 - 6758d - d2 = 74256.25d
*transpose right side eqtn to the left and combine like terms
d2 + 67498.25d -11417641 = 0
*Using this formula :
You will get 2 answers, 1 positive and 1 negative. The answer is the positive value which is 169ft (rounded off)
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