Answer:
If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, it will take 140 hours to fill the pool
Step-by-step explanation:
An inlet pipe can fill the pool in hours = 20
Inlet pipe 1 hour work = [tex]\frac{1}{20}[/tex]
A drain pipe can empty the pool in 21 hours
Drain pipe 1 hour work =[tex]\frac{1}{21}[/tex]
Inlet pipe and drain pipe 1 hour together work = [tex]\frac{1}{20}-\frac{1}{21}=\frac{1}{420}[/tex]
Now we are given that the pool is 2/3 filled
So, remaining portion to be filled =[tex]1 - \frac{2}{3} = \frac{1}{3}[/tex]
So, Inlet pipe and drain pipe fill [tex]\frac{1}{420}[/tex] in hours = 1
So, they can fill 1/3 in hours = [tex]\frac{1}{\frac{1}{420}} \times \frac{1}{3} =140 hours[/tex]
Hence If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, it will take 140 hours to fill the pool
