Question

Two pipes A and B can fill a tank in 24 minutes and 32 minutes, respectively. Initially, both pipes are opened simultaneously. After how many minutes should pipe B be turned off so that the tank is full in 18 minutes?

Solution

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Pipe A run for 18 minutes. Because pipe A can fill a whole tank in 24 minutes, if pipe A work 18 minutes she can fill

18 minutes24minuites per tank=34 tank\dfrac{18\text{ minutes}}{24 \text{minuites per tank}}=\dfrac{3}{4}\text{ tank}

So, for 18 minutes pipe A can fill 34\dfrac{3}{4} of a tank.

14\dfrac{1}{4} tank will need to fill pipe B.

Because pipe B can fill a whole tank in 32 minutes, to fill 14\dfrac{1}{4} tank she needs one-fourth of 32 minutes because pipe need to fill 14\dfrac{1}{4} tank, not a whole tank.

324=8 minutes\dfrac{32}{4}=8\text{ minutes}

To fill a tank for 18 minutes if pipe A work all the time(18 minutes), after 8 minutes pipe B should be turned off.

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