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The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?

(A) 0.22
(B) 0.31
(C) 2.50
(D) 3.21
(E) 4.56

Respuesta :

JeanaShupp

Answer: (D) 3.21

Step-by-step explanation:

Let [tex]t_A=[/tex] Time taken by one outlet to fill the pool.

[tex]t_B=[/tex]Time taken by second outlet to fill the pool.

Given : The time taken by one outlet to fill the entire pool : [tex]t_A=[/tex] 9 hours

The time taken by second outlet to fill the entire pool : [tex]t_B=[/tex] 5 hours

Now , if both outlets are used at the same time, approximately what is the number of hours required to fill the pool (T) , then the time required to fill the pool will be :_

[tex]\dfrac{1}{T}=\dfrac{1}{t_A}+\dfrac{1}{t_B}\\\\\Rightarrow =\dfrac{1}{T}=\dfrac{1}{9}+\dfrac{1}{5}\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{9+5}{(9)(5)}=\dfrac{14}{45}\\\\\Rightarrow\ T=\dfrac{45}{14}=3.21428571429\approx3.21[/tex]

Hence, the approximate time taken by both outlets to fill the pool together = 3.21 hours.

Thus , the correct option is  (D) 3.21

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