It will take 6 minutes to drain the pool.
As the problem states the height of the water in an above ground pool is 3ft. In other word:
The pool needs to be drained at a Rate of Change of 1/2 inches per minutes. In other words:
Therefore, we can write an equation as:
[tex]h=3-\frac{1}{2}t \\ \\ \\ h:Height \\ \\ t:time \\ \\ \\ The \ slope \ is \ negative \ because \ the \ pool \ needs \ to \ be \ drained[/tex]
To drain the pool implies that we don't have any water in the pool, in other words this is true if and only if:
[tex]h=0[/tex]
So:
[tex]h=3-\frac{1}{2}t \\ \\0=3-\frac{1}{2}t \\ \\ \\ Solving \ for \ t: \\ \\ \frac{1}{2}t=3 \\ \\ t=6[/tex]
So, it will take 6 minutes to drain the pool.
Average Rate of Change: https://brainly.com/question/14196399#
#LearnWithBrainly
Answer: It would take 72 minutes.
Step-by-step explanation:
The data is:
The height of the water in the pool is 3 feet.
The water is drained by a height of 1/2 inches per minute.
We want to calculate how much time it will need to fully drain the pool.
The first thing we always need to do is have al our data in the same units, so here we need to transform feet into inches:
1 feet = 12 inches
then 3 feet = 3*12 inches = 36 inches.
Now we have that the equation that describes the height of the water in the pool is:
h = (36 - (1/2)*m) inches
where m is the number of minutes since we started draining the pool.
And the pool will be fully drained when h = 0, so we need to solve the equation:
0 = 36 - (1/2)*m
(1/2)*m = 36
m = 36*2 = 72 minutes
