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

Answer: (D) 3.21Step-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 hoursThe time taken by second outlet to fill the entire pool : [tex]t_B=[/tex] 5 hoursNow , 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