Answer:
It take 37.5 hours to fill the tank
Step-by-step explanation:
Given:
Time Taken to fill the tank = 15 hours
Time Taken to empty the tank = 25 hours
To Find:
Time taken to fill the tank when both the inlet and outlet is opened at the same time = ?
Solution:
Let the time to fill the tank be x
In 15 hours the tap fills the tank
Rate at which the tank is filled = [tex]\frac{1}{15}[/tex]
In 25 hours the tap empties the tank
Rate at which the tank is drained = [tex]\frac{1}{25}[/tex]
The net gain per minute on the total filling rate is
=> [tex]\frac{1}{x} =[/tex] Rate at which the tank is filled - Rate at which the tank is drained
=>[tex]\frac{1}{x} = \frac{1}{15} - \frac{1}{25}[/tex]
=>[tex]\frac{1}{x} = \frac{25-15}{15 \times 25} [/tex]
=>[tex]\frac{1}{x} = \frac{10}{375} [/tex]
=> 10x = 375
=>[tex]x = \frac{375}{10}[/tex]
=>x = 37.5
