Two pipes are used to fill the astern completely. The second pipe opened one hour after the
first pipe. Three hours after the first plpe has opened, there is still (9/20) of the cistern is to
be filled. When the cistern is completely filled, it was found that each pipe has filled half of
the astern. How many hours would it take each one to completely filled the cistem
individually?
Answers
Given : second pipe opened one hour after the first pipe. Three hours after the first plpe has opened, there is still (9/20) of the cistern is to
be filled. When the cistern is completely filled, it was found that each pipe has filled half of the cistern
To find : How many hours would it take each one to completely filled the cistern individually
Solution:
Let say Pipe A fill Cistern in A hrs
pipe A fills in 1 hr = 1/A
Let say Pipe B fill Cistern in B hrs
pipe B fills in 1 hr = 1/B
3/A + 2/B = 1 - 9/20
=> 3/A + 2/B = 11/20
Let say Cistern filled in n+ 1 hrs
Then (n + 1)/A = n/B = 1/2
=> A = 2(n + 1)
B = 2n
3/A + 2/B = 11/20
=> 3/2(n +1) + 2/2n = 11/20
=> 3/(n + 1) + 2/n = 11/10
=> 30n + 20n + 20 = 11n² + 11n
=> 11n² - 39n - 20 = 0
=> 11n² - 44n + 5n - 20 = 0
=> 11n(n - 4) + 5(n - 4) = 0
=> (11n + 5) (n - 4) = 0
=> n = 4
A = 2(n + 1) = 10
B = 2n = 8
Pipe A will fill in 10 hrs & pipe B will fill in 8 hrs
Learn more:
Pipe a can fill a cistern in 6 hours and pipe B can fill it in 8 hour both ...
https://brainly.in/question/11594393
Pipe a and b can fill the tank in 6 minutes and 7 minute repectively ...
https://brainly.in/question/8175617
In the kitchen there are two pipes A and B. Pipe B take 5 more ...
https://brainly.in/question/13990751