Two pumps

Pump A takes twice as long to fill a tank than B . Together they take 2 hours to fill the tank. How long does each one take to fill the tank by itself?

Result

A =  6 h
B =  3 h

Solution:

A=2B 1/A+1/B=1/2 1/A+2/A=1/2 3/A=1/2 A=3 2=6=6  h A = 2B \ \\ 1/A + 1/B = 1/2 \ \\ 1/A + 2/A = 1/2 \ \\ 3/A = 1/2 \ \\ A = 3 \cdot \ 2 = 6 = 6 \ \text{ h }
B=A/2=6/2=3=3  h   s=2 (1A+1B)=2 (16+13)=1B = A/2 = 6/2 = 3= 3 \ \text{ h } \ \\ \ \\ s = 2 \cdot \ (\dfrac{ 1 }{ A } + \dfrac{ 1 }{ B } ) = 2 \cdot \ (\dfrac{ 1 }{ 6 } + \dfrac{ 1 }{ 3 } ) = 1



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