Question

Pipe A is an inlet pipe that can fill an empty cistern in 8.7 hours. Pipe B can drain a filled
cistern in 5.8 hours. When the cistern was filled the two pipes are opened one at a time
for an hour each, starting with Pipe B. How long will it take for the cistern to be empty?
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Answer 1

Answer:

30.8 Hrs

Step-by-step explanation:

Pipe A is an inlet pipe that can fill an empty cistern in 8.7 hours. Pipe B can drain a filled  cistern in 5.8 hours. When the cistern was filled the two pipes are opened one at a time  for an hour each, starting with Pipe B. How long will it take for the cistern to be empty?

Pipe B can drain a filled  cistern in 5.8 hours

in 1st hour Cistern by B  is emptied = 1/5.8

in Next two hours cistern is emptied by   1/5.8  - 1/8.7

= (1/17.4)(3 - 2)

= 1/17.4

In each next two hrs it emptied by 1/17.4

Let say it taken 2n  hrs  ( n such rounds)

1/5.8  +  n/17.4   = 1    

=> (1/17.4)(3 + n) =  1

=> 3 + n = 17.4

=> n = 14.4

for n = 14   (  1+ 2*14 = 29 hrs)

cistern is emptied 1/5.8 + 14/17.4

in 30th hr it is filled 1/8.7  again

so after 30 hr cistern has been emptied by

= 1/5.8 + 14/17.4 - 1/8.7

= 15/17.4

Remaining water in cistern  1 - 15/17.4

= 2.4/17.4

1 is  drained in  5.8 hrs

2.4/17.4 is drained by Pipe B in     (2.4/17.4) * 5.8  =  0.8 hrs

Hence total = 30.8 Hrs

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