Verified answer

The intake pipe can fill a certain tank in 6 hours when the outlet pipe is closed, but with the outlet pipe open it takes 9 hours. How long would it take the outlet pipe to empty a full tank?

:

Let x = time for outlet to empty the tank:

:

Let the filled tank = 1

:

The intake is filling for 9 hrs (+)

The outlet is draining for 9 hrs (-)

9%2F6+-+9%2Fx = 1

:

Multiply the equation by 6x to get rid of the denominators

9x - 6(9) = 6x

9x - 54 = 6x

9x - 6x = 54

3x = 54

x = 54/3

x = 18 hrs for the outlet to empty a full tank by itself

:

Check: 9/6 - 9/18 =

3/2 - 1/2 = 1

:

Another words:

the input will fill a tank and a half in 9 hrs

the outlet will remove a half a tank in 9 hrs

Leaving a full tank

:

9[(1/6)-(1/x)]=1

(x-6)/6x=1/9

6x=9x-54

54=3x

18=x

18 hours