Question

Pipe A can fill a tank in 5 hours. Pipe B can fill it in 2 hours less time than it takes pipe C, a draining pipe, to empty the tank. With all 3 pipes open, it takes 3 hours to fill the tank. How long will it take pipe C to empty it?

Answer 1

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

$\dfrac15+\dfrac1{x-2}-\dfrac1x=\dfrac 13\\\\\Rightarrow\ \dfrac{x-(x-2)}{x(x-2)}=\dfrac13-\dfrac15\\\\\Rightarrow\ \dfrac{x-x+2}{x^2-2x}=\dfrac{5-3}{15}\\\\\Rightarrow \dfrac{2}{x^2-2x}=\dfrac2{15}\\\\\Rightarrow\ x^2-2x=15\\\\\Rightarrow\ x^2-2x-15=0\\\\\Rightarrrow\ x^2-5x+3x-15=0\\\\\Rightarrow\ x(x-5)+3(x-5)=0\\\\\Rightarrow\ (x-5)(x+3)=0\\\\\Rightarrow\ x=5, -3$

Time cannot be negative,

So, x=5

Thus, Time taken by pipe C to empty the tank = 5 hours.