Question

Tap a can fill a cistern in 12 hours, b in 10 hours and c in 15 hours. they all are opened together, but a is closed after 2 hours of starting and b is closed 3 hours before the cistern to be filled. in how much time will the cistern be filled?

Answer 1

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Given: Tank of volume X

Constant flowrates (tank volumes per hour)

A=X/3

B=X/5

C= -X/7 1/7

Find: t the time in hours to fill the tank

Solution:

(A + B + C) * t= X

(X/3 + X/5 -X/7 1/7) * t= X

(X/3 + X/5 - 7X/50) * t = X

((50 X + 30X -21X)/150) * t = X

(59X/150) *t = X

Divide both sides by X

59/150 * t = 1

t = 1/(59/150)

t= 150/59

Therefore the time to fill the tank is 150/59 hours or 2.54 hours

Answer 2

the time to fill the tank is 2.54 hours