Answer: Time taken by pipe C to empty the tank = 5 hours.
Step-by-step explanation:
Pipe A can fill a tank in 5 hours.
Let time taken by Pipe C = x ( hours)
Time taken by Pipe B = x-2 ( hours)
Now, with all 3 pipes open, it takes 3 hours to fill the tank, it can be represented as
[tex]\dfrac15+\dfrac1{x-2}-\dfrac1x=\dfrac 13\\\\\Rightarrow\ \dfrac{x-(x-2)}{x(x-2)}=\dfrac13-\dfrac15\\\\\Rightarrow\ \dfrac{x-x+2}{x^2-2x}=\dfrac{5-3}{15}\\\\\Rightarrow \dfrac{2}{x^2-2x}=\dfrac2{15}\\\\\Rightarrow\ x^2-2x=15\\\\\Rightarrow\ x^2-2x-15=0\\\\\Rightarrrow\ x^2-5x+3x-15=0\\\\\Rightarrow\ x(x-5)+3(x-5)=0\\\\\Rightarrow\ (x-5)(x+3)=0\\\\\Rightarrow\ x=5, -3[/tex]
Time cannot be negative,
So, x=5
Thus, Time taken by pipe C to empty the tank = 5 hours.
