SOLUTION: A cistern can be filled by two pipes. The small pipe alone will take 24 minutes longer than larger pipe to fill cistern alone.the small pipe will take 32 minutes longer to fill cis

Question 1095982: A cistern can be filled by two pipes. The small pipe alone will take 24 minutes longer than larger pipe to fill cistern alone.the small pipe will take 32 minutes longer to fill cistern alone than when two pipes are operating together.How long will it take larger pipe to fill the cistern alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A cistern can be filled by two pipes.
The small pipe alone will take 24 minutes longer than larger pipe to fill cistern alone.
the small pipe will take 32 minutes longer to fill cistern alone than when two pipes are operating together.
How long will it take larger pipe to fill the cistern alone?
:
let x = time for the larger pipe to fill the cistern alone
then
(x+24) = time for the small pipe alone
:
"the small pipe will take 32 minutes longer to fill cistern alone than when two pipes are operating together."
therefore
(x+24)-32 = (x-8) = time required when working together
let the completed job = 1 (a full cistern)
+ = 1
multiply x(x+24), cancel the denominators
(x+24)(x-8) + x(x-8) = x(x+24)
x^2 - 8x + 24x - 192 + x^2 - 8x = x^2 + 24x
combine like terms on the left
x^2 + x^2 - x^2 - 8x - 8x + 24x - 24x - 192 = 0
x^2 - 16x - 192 = 0
You can use the quadratic formula; a=1; b=-16; c=-192 but this will factor
(x-24)(x+8) = 0
The positive solution
x = 24 min the large pipe alone to fill the cistern
:
:
Check this. together 16 min; small pipe 48 min
+ = 1
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