# Three pumps together

One pump fills the tank in 1.5 hours, the second in 2 hours, and the third in 3 hours 20 minutes. How many minutes will the tank fill with three pumps if they work simultaneously?

Result

t =  40.909 min

#### Solution:

$a=1.5 \ h=1.5 \cdot \ 60 \ min=90 \ min \ \\ b=2 \ h=2 \cdot \ 60 \ min=120 \ min \ \\ c=h_{2}min(3+20/60)=200 \ \\ \ \\ s=\dfrac{ 1 }{ a } + \dfrac{ 1 }{ b } + \dfrac{ 1 }{ c }=\dfrac{ 1 }{ 90 } + \dfrac{ 1 }{ 120 } + \dfrac{ 1 }{ 200 } \doteq \dfrac{ 11 }{ 450 } \doteq 0.0244 \ \\ \ \\ t=1/s=1/0.0244 \doteq \dfrac{ 450 }{ 11 } \doteq 40.9091 \doteq 40.909 \ \text{min}$

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