Question
Pipe $A$ can fill an empty tank in $5$ hours while pipe $B$ can empty the full tank in $6$ hours. If both are opened at the same time in the empty tank, how much time will they take to fill it up completely?
✓
Answer
Pipe $A's$ one hour's work for filling the tank $=\frac{1}{5}$
Pipe $B's$ one hour's work for emptying $=\frac{1}{6}$
Both pipes are opened, then,
Both's one hour's work $=\frac{1}{5}-\frac{1}{6}$
$=\frac{6-5}{30}=\frac{1}{30}$
$\therefore$ The empty tank will be filled in $30$ hours.
Pipe $B's$ one hour's work for emptying $=\frac{1}{6}$
Both pipes are opened, then,
Both's one hour's work $=\frac{1}{5}-\frac{1}{6}$
$=\frac{6-5}{30}=\frac{1}{30}$
$\therefore$ The empty tank will be filled in $30$ hours.
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