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 minute

Question 1185242: 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.
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.
let x = time required by the larger pipe alone
:
The small pipe alone will take 24 minutes longer than the larger pipe to fill the cistern alone.
(x+24) = time required by the smaller pipe
:
The small pipe alone will take 32 minutes longer to fill the cistern alone than when the two pipes are operating together.
let t = time required when working together
then
t + 32 = x+24
t = x + 24 - 32
t = x - 8, time required when working together
:
Let the full cistern = 1
+ = 1
multiply by x(x+24)
(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 + 24x - 8x - 24x - 192 = 0
x^2 - 16x - 192 = 0
a quadratic equation which we can factor
(x-24)(x+8) = 0
positive solution
x = 24 min, large pipe working alone
:
:
Check solution
small pipe alone: 24 + 24 = 48 min
working together: 24 - 8 = 16 min
+ =
+ = 1

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