A large pool has a faucet to allow water to enter the pool and a drain to allow water to leave the pool. The change in the amount of water in the pool after [tex]\mathbf{1 \dfrac{1}{2} \ minutes}[/tex] in mixed number is [tex]\mathbf{5 \dfrac{1}{5} \ gallons \ of \ water}}[/tex].
From the given information:
At the Inlet:
At the Outlet:
The change in the amount of water in the pool is the difference between the Outlet and the Inlet.
i.e.
[tex]= \mathbf{\Big (15 \dfrac{2}{3}- 12\dfrac{1}{5} \Big) \ gallons \ of \ water}[/tex]
[tex]= \mathbf{\Big (\dfrac{47}{3}- \dfrac{61}{5} \Big) \ gallons \ of \ water} \\ \\ \\ =\mathbf{\dfrac{235 - 183}{15}\ gallons \ of \ water} \\ \\ \\ = \mathbf{\dfrac{52}{15}\ gallons \ of \ water}[/tex]
For each minute, [tex]\mathbf{\dfrac{52}{15}}[/tex] gallons of water leaves the tank;
∴
For [tex]\mathbf{1 \dfrac{1}{2} \ minutes}[/tex], the amount of water that will leave the tank will be:
[tex]= \mathbf{ \dfrac{1 \dfrac{1}{2} \ minutes \times \dfrac{52}{15} \ gallons \ of \ water}{ 1 \ minute}}[/tex]
[tex]= \mathbf{ \dfrac{ \dfrac{3}{2} \ minutes \times \dfrac{52}{15} \ gallons \ of \ water}{ 1 \ minute}}[/tex]
[tex]= \mathbf{ \dfrac{26}{5} \ gallons \ of \ water}}[/tex]
[tex]= \mathbf{5 \dfrac{1}{5} \ gallons \ of \ water}}[/tex]
Therefore, we can conclude that the change in the amount of water in the pool after [tex]\mathbf{1 \dfrac{1}{2} \ minutes}[/tex] in mixed number is [tex]\mathbf{5 \dfrac{1}{5} \ gallons \ of \ water}}[/tex].
Learn more about fractions here:
https://brainly.com/question/6201432?referrer=searchResults
Answer:
-2 3/8
Step-by-step explanation:
i took k12 quiz
