it will take 20 hours to fill the tank if both pipes are open
Explanation:The time it takes to fill the tank = 10 hours
In 1 hour, it will take = 1/10 hours
The time it takes for the outlet to empty the tank = 2 times the time it takes to fill the tank
The time it takes for the outlet to empty the tank = 2 × 10 = 20 hours
In 1 hour, it will take = 1/20 hours
If both pipes are open, let the time it will take to fill the tank be t hours
In 1 hour = 1/t hours
The change in the amount in the tank is equal to the time it will take to fill the tank
1/10 - 1/20 = 1/t
[tex]\begin{gathered} \frac{1}{10}-\frac{1}{20}=\frac{1}{t} \\ \frac{2(1)\text{ -1(1)}}{20}=\frac{1}{t} \\ \frac{2-1}{20}=\frac{1}{t} \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{1}{20}=\frac{1}{t} \\ \text{cross multiply:} \\ 1(t)\text{ = 1(20)} \\ t\text{ = 20} \end{gathered}[/tex]Hence, it will take 20 hours to fill the tank if both pipes are open
