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Vesnalui [34]
3 years ago
14

An inlet pipe can fill a swimming pool in 9 hours and an outlet pipe can empty the pool in 12 hours. Through an error, both pipe

s are left open. How long will it take to fill te pool?
Mathematics
1 answer:
Andrew [12]3 years ago
7 0

Answer:

36 hours.

Step-by-step explanation:

Let x represent time taken by both pipes to fill the tank.

We have been given that an inlet pipe can fill a swimming pool in 9 hours. So part of pool filled by inlet pipe in one hour would be \frac{1}{9}.

We are also told that an outlet pipe can empty the pool in 12 hours. The part of pool emptied by outlet pipe in one hour would be \frac{1}{12}.

Sine the time taken by both pipes to fill the tank is x hours, so part of pool filled by both pipes in one hour would be \frac{1}{x}.

We will get an equation using our given information as:

\frac{1}{x}=\frac{1}{9}-\frac{1}{12}

Let us solve for x.

\frac{1}{x}=\frac{1*12}{9*12}-\frac{1*9}{12*9}

\frac{1}{x}=\frac{12}{108}-\frac{9}{108}

\frac{1}{x}=\frac{12-9}{108}

\frac{1}{x}=\frac{3}{108}

Cross multiply:

3x=108

\frac{3x}{3}=\frac{108}{3}

x=36

Therefore, it will take 36 hours for both pipes to fill the tank.

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