SOLUTION: A rectangular tank can be filled with water by two pipes in 11-1/9 minutes. If the larger pipe alone takes 5 minutes less to fill the tank than the smaller pipe,find the time each

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Question 209637: A rectangular tank can be filled with water by two pipes in 11-1/9 minutes. If the larger pipe alone takes 5 minutes less to fill the tank than the smaller pipe,find the time each pipe takes to fill the tank.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular tank can be filled with water by two pipes in 11-1/9 minutes.
If the larger pipe alone takes 5 minutes less to fill the tank than the smaller pipe,
find the time each pipe takes to fill the tank.
:
Convert 111%2F9 to an improper fractions: 100%2F9 minutes
:
Let t = large pipe time alone
then
(t+5) = small pipe time alone
:
Let the completed job = 1; (full tank)
:
%28100%2F9%29%2Ft + %28100%2F9%29%2F%28%28t%2B5%29%29 = 1
:
multiply equation by t(t+5), results
%28100%28t%2B5%29%29%2F9 + %28100t%29%2F9 = t(t+5)
:
%28%28100t%2B500%29%29%2F9 + %28100t%29%2F9 = t^2 + 5t
Multiply eq by 9, results
100t + 500 + 100t = 9(t^2 + 5t)
:
200t + 500 = 9t^2 + 45t
A quadratic equation:
9t^2 + 45t - 200t - 500 = 0
:
9t^2 - 155t - 500 = 0
Factors to:
(9t + 25)(t - 20) = 0
the positive solution:
t = 20 minutes, the large pipe alone
then
20 + 5 = 25 min the small pipe
;
:
Check solution using a decimal for that annoying fraction
11.11/20 + 11.11/25
.555 + .444 = .999 ~ 1