SOLUTION: A small pipe can fill a tank in 8 min more time than it takes a larger pipe to fill the same tank. Working together, the pipes can fill the tank in 3 min. How long would it take ea

Question 1003410: A small pipe can fill a tank in 8 min more time than it takes a larger pipe to fill the same tank. Working together, the pipes can fill the tank in 3 min. How long would it take each pipe, working alone, to fill the tank?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A small pipe can fill a tank in 8 min more time than it takes a larger pipe to fill the same tank.
Working together, the pipes can fill the tank in 3 min.
How long would it take each pipe, working alone, to fill the tank?
:
let t = time for the larger pipe to fill the tank alone
then
(t+8) = time for the smaller pipe to do it
:
let the completed job = 1 (a full tank)
+ = 1
multiply by t(t+8), cancel the denominators and you have
3(t+8) + 3t = t(t+8)
3t + 24 + 3t = t^2 + 8t
Combine like terms on the right
0 = t^2 + 8t - 6t - 24
A quadratic equation
t^2 + 2t - 24 = 0
Factors to
(t+6)(t-4) = 0
We only want the positive solution here
t = 4 min for the larger pipe to fill the tank
:
:
Check solution (small pipe requires 12 min)
+ = 1

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