Question

There are two pipes $A$ and $B$ connected to a tank. It is known that $A$ can fill the tank in $4$ hours while $B$ can empty the tank in $6$ hours. If both the pipes are opened together, how much time will it take to fill up the tank?

Answer 1

If $t$ is the time to fill the tank when both$A$ and $B$ are operative, then
$\frac{1}{t}=\frac{1}{4}-\frac{1}{6}=\frac{1}{12}$.
Hence, $t=12$. Thus the tank get filled in $12$ hours.