Pipe $A$ can fill a tank in $5$ $hours$,pipe $B$ in $10$ $hours$,and pipe $C$ in $30$ $hours$. If all the pipes are opened,in how many $hours$ will the tank be filled?

$A$ tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank $5$ $hours$ faster than the first pipe and $4$ $hours$ slower than the third pipe. The time (in $hours$) required by the first pipe is:

$A$ tank can be filled by pipe $A$ in $2$ $hours$ and pipe $B$ in $6$ $hours.$ At $10 \, am$ pipe $A$ was opened. At what time will the tank be filled if pipe $B$ is opened at $11 \, am$?

Two pipes $A$ and $B$ can fill a tank in $30$ $minutes$ and $45$ $minutes$ respectively. Pipe $C$ can empty the tank in $36$ $minutes$. Initially,pipes $A$ and $B$ are opened. After $12$ $minutes$,pipe $C$ is also opened. What is the total time (in $minutes$) required to fill the tank?

$A$ tank is filled in $5$ $hours$ by three pipes $A, B$ and $C$. The pipe $C$ is twice as fast as $B$ and $B$ is twice as fast as $A$. How much time (in $hours$) will pipe $A$ alone take to fill the tank?

$A$ pump can fill a tank with water in $2$ $hours$. Because of a leak,it took $2 \frac{1}{3}$ $hours$ to fill the tank. The leak can drain all the water of the tank in (in $hours$)?