# Number of Hours for Pipe to Fill the Tank if the Drain is Closed

**Problem 1**

A pipe can fill a tank in 3 hours if the drain is open. If the pipe runs with the drain open for 1 hour and the drain is then closed, the tank will be filled in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed?

**Answer Key**

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**Solution**

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*x*

rate of drain = -1/

*y*

A pipe can fill a tank in 3 hours if the drain is open

$\dfrac{1}{x} - \dfrac{1}{y} = \dfrac{1}{3}$

the pipe runs with the drain open for 1 hour

$\left( \dfrac{1}{x} - \dfrac{1}{y} \right)(1)$

If the pipe runs with the drain open for 1 hour and the drain is then closed, the tank will be filled in 40 minutes more

$\dfrac{1}{3}(1) + \dfrac{1}{x} \left( \dfrac{40}{60} \right) = 1$

$\dfrac{1}{x} = 1$

$x = 1 ~ \text{hr}$ ← *answer*

**Problem 2**

A pipe can fill a tank in 4 hours if the drain is open. The tank is initially empty. If the pipe runs with the drain open for 1 hour and the pipe is then closed, the tank will be emptied in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed?

**Answer Key**

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**Solution**

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*x*

rate of drain = -1/

*y*

A pipe can fill a tank in 4 hours if the drain is open

$\dfrac{1}{x} - \dfrac{1}{y} = \dfrac{1}{4}$ ← Eq. (1)

the pipe runs with the drain open for 1 hour

$\left( \dfrac{1}{x} - \dfrac{1}{y} \right)(1)$

If the pipe runs with the drain open for 1 hour and the pipe is then closed, the tank will be emptied in 40 minutes more

$\dfrac{1}{4}(1) - \dfrac{1}{y} \left( \dfrac{40}{60} \right) = 0$

$\dfrac{1}{y} = \dfrac{3}{8}$

From Eq. (1)

$\dfrac{1}{x} - \dfrac{3}{8} = \dfrac{1}{4}$

$\dfrac{1}{x} = \dfrac{5}{8}$

$x = 1.6 ~ \text{hrs}$ ← *answer*

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