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

rate of pipe = 1/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

rate of pipe = 1/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