# Three pumps

The water tank is emptied with the first pump in 6 hours, with the second pump in 2 hours. In order to be emptied in 1 hour, all three pumps had to be started at once. How long will take tank be emptied by only the third pump?

Result

c =  3 h

#### Solution:

$1 \cdot \ (1/6 + 1/2 + 1/c)=1 \ \\ c/6 + c/2 + 1=c \ \\ 0.333333c=1 \ \\ \dfrac{ 1 }{ 3 }c=1 \ \\ c=3 \ \\ =3 \ \text{h}$

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