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

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Question 1169855: A cistern can be filled by two pipes. The small pipe alone will take 24 minutes
longer than the larger pipe to fill the cistern alone. The small pipe alone will take 32 minutes longer to fill the cistern alone than when the two pipes are operating together. How long will it take the larger pipe to fill the cistern alone
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
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 the larger pipe to fill the cistern alone.
let b = the larger pipe time to fill the cistern alone
then
(b+24) = time the small pipe to do it
let t = time required by the two pipes working together
let the completed job = 1
+ = 1
:
The small pipe alone will take 32 minutes longer to fill the cistern alone than when the two pipes are operating together.
t = (b+24) - 32
t = (b-8)
How long will it take the larger pipe to fill the cistern alone.
+ = 1
Replace t with (b-8)
+ = 1
multiply equation by b(b+24)
(b-8)(b+24) + b(b-8) = b(b+24)
FOIL
b^2 + 24b - 8b - 192 + b^2 - 8b = b^2 + 24b
Cancel a b^2 and a 24b and we have
b^2 - 16b - 192 = 0
This will factor to
(b+8)(b-24) = 0
positive solution
b = 24 min for the large pipe to fill the cistern alone
:
:
Check this in the equation
+ = 1
t = 24 - 8
t = 16 min together
and
24 + 24 = 48 min small pipe alone
+ = 1
+ = 1

Answer by MathTherapy(10552) (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 the larger pipe to fill the cistern alone. The small pipe alone will take 32 minutes longer to fill the cistern alone than when the two pipes are operating together. How long will it take the larger pipe to fill the cistern alone

Let time it takes large pipe to fill cistern, be L Then, large pipe can to fill of cistern, in 1 minute Also, time it takes small pipe to fill cistern = L + 24 Thus, small pipe can fill of cistern in 1 minute In addition, time taken by both to fill cistern: L + 24 - 32, or L - 8 Therefore, both pipes can fill of cistern in 1 minute We then get: (L + 24)(L - 8) + L(L - 8) = L(L + 24) -------- Multiplying by LCD, L(L + 24)(L - 8) (L - 24)(L + 8) = 0 Time it takes larger pipe to fill cistern, or OR L = - 8 (ignore) You can do the CHECK!!