It takes 20 hours to fill the pool using the first hose. It takes 16 hours to fill the pool using the second hose. How long would it take if you used both?

Answer: 8 [tex]\frac{8}{9}[/tex] hoursStep-by-step explanation:Let x represent the time it takes if both are used.The unit time it takes to fill the pool using the first house is 1/20 and also the unit time it takes to fill the pool using the second house is 1/16 , therefore:1/16 + 1/20 = 1/x[tex]\frac{4+5}{20}[/tex] = [tex]\frac{1}{x}[/tex][tex]\frac{9}{80}[/tex] = [tex]\frac{1}{x}[/tex]Thereforex = [tex]\frac{80}{9}[/tex]Therefore, it takes 8 [tex]\frac{8}{9}[/tex] hours using both houses