SOLUTION: I keep getting the incorrect answer to the following problem, I'm not sure where my error was, can you help me? One method for determining the depth of a well is to drop a ston

Question 196647: I keep getting the incorrect answer to the following problem, I'm not sure where my error was, can you help me?
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 = 16t1^2, 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 2.3 s? (Round the answer to the nearest whole number.)
thanks!
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since the "total time is 2.3 s", this means that

Start with the given equation.

Plug in

Multiply EVERY term by the LCD to clear out the fractions.

Multiply and simplify

Subtract 2d from both sides.

Square both sides

Square to get

FOIL the left side

Get all terms to the left side.

Combine like terms.

Notice we have a quadratic in the form of where , , and

Let's use the quadratic formula to solve for d

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

So the answers are or

which approximate to or

Notice that if the time for the stone to fall was 2.3 seconds, then the depth would be AT MOST . In other words, the MAX depth that is possible in this problem is about 85 feet.

Since the value is too large, this means that is the only answer.

So to the nearest whole number, the depth of the well is about 79 feet.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
t1 + t2 = √d/4 + d/1090
How deep is the well if this total time is 2.3 s? (Round the answer to the nearest whole number.)
--------------
2.3 = sqrt(d)/4 + d/1090
sqrt(d)/4 = 2.3 - d/1090
d/16 = 5.29 - 4.6d/1090 + d^2/1090^2
d^2 + 5.29*1090^2 - 4.6d*1090 - d*1090^2/16 = 0
d^2 - d*(5014 + 74256.25) + 6285049 = 0
d^2 - 79270.25d + 6280549 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=6258650339.0625 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 79190.9410674966, 79.3089325033652. Here's your graph:

79 feet looks right.

RELATED QUESTIONS
I keep getting the incorrect answer to the following problem, I'm not sure where my error (answered by edjones)
Good evening tutor, Could you explain to me how to solve this problem. I am sure the (answered by stanbon)
I need help. I'm correcting a test and I keep getting the same answer that I had gotten... (answered by sofiyac)
Hi! On the following problem I keep getting the incorrect answer. I think I'm close to (answered by Alan3354,jim_thompson5910)
log 3x = log 5 + log (x - 2) I think I am getting this. But when I follow the... (answered by Edwin McCravy,kmadison)
Hello, I'm in my last week of my intermediate algebra class and need an additional 14... (answered by Alan3354)
I am stuck on a question about exponential expressions and the order of operations. I... (answered by jim_thompson5910)
Five eighths of the 4960 voters supported Mayor Rios. answer:3100 a.) How many voters... (answered by checkley71,ilana)
My school wants me to simplify the expression. But I'm not sure how to I keep trying but... (answered by sudhanshu_kmr)