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Filling a cistern

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Pipe A alone fills an empty cistern in $6$ hours, and pipe B alone fills it in $3$ hours. Each pipe always pours at its own constant rate. If both pipes are opened together on the empty cistern, how many hours does it take to fill it?

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Hint

Add the fractions of the cistern each pipe fills in one hour.

Solution

In one hour pipe A fills $\frac{1}{6}$ of the cistern and pipe B fills $\frac{1}{3}$ .
Together they fill $\frac{1}{6} + \frac{1}{3} = \frac{1}{2}$ of the cistern per hour.
So the full cistern takes $1 \div (\frac{1}{2}) = 2$ hours, and the answer is $2$ .

Answer: $2$

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