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A pipe can fill a cistern in 3 hoursdue to leak in the bottom it is filled in four hourswhen the cistern is full in How to find out how muchtime will it be emptied by the leak​

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Answer:

Let V = volume of cistern, gal

RateP = volumetric rate of fill pipe, gal/min

tP = 10 hrs (time to fill V with no leaks)

V = RateP × tP

or RateP = V/tP

also,

V = RateL × t

where: RateL = volumetric leak rate, gal/min

t = time to drain V alone = ?

and RateL = V/t

Combined balance with both fill and leak pipes open:

V = RateP×(12 hr) - RateL×(12 hr)

V = (V/tP)×(12 hr) - (V/t)×(12 hr)

and solve for t:

1/(12 hr) = 1/tP - 1/t

1/t = 1/tP - 1/(12 hr) = 1/(10 hr) - (1/12 hr)

t = 1/( 1/(10 hr) - 1/(12 hr) ) = 60 hr

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