Respuesta :
Answer:
It will take 15 hours to fill the tank with both valves open
Step-by-step explanation:
Given,
The time taken by inlet pipe to fill the tank = 10 hours,
So, work done by inlet pipe in one hour = [tex]\frac{1}{10}[/tex],
Also, the time taken by outlet pipe to drain = 30 hours,
So, work done by outlet pipe in one hour = [tex]-\frac{1}{30}[/tex],
( Note : Negative sign shows the draining )
Thus,the total work done in one hour
[tex]=\frac{1}{10}-\frac{1}{30}[/tex]
[tex]=\frac{3-1}{30}[/tex]
[tex]=\frac{2}{30}[/tex]
[tex]=\frac{1}{15}[/tex]
Hence, the time taken to fill the tank = [tex]\frac{1}{\text{Total work done in one hour}}[/tex]
[tex]=\frac{1}{1/15}[/tex]
= 15 hours
