# 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:

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

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