SOLUTION: 3. A tank has two drains. One drain takes 16 minutes longer to empty the tank than does a second drain. With both drains open, the tank is emptied in 6 minutes. How long would it t

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Question 1196841: 3. A tank has two drains. One drain takes 16 minutes longer to empty the tank than does a second drain. With both drains open, the tank is emptied in 6 minutes. How long would it take each drain, working alone, to empty the tank?
Answer by ankor@dixie-net.com(22740) (Show Source):
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3. A tank has two drains.
One drain takes 16 minutes longer to empty the tank than does a second drain.
With both drains open, the tank is emptied in 6 minutes.
How long would it take each drain, working alone, to empty the tank?
:
let t = time required by the 2nd drain to empty the tank
the 1st drain takes 16 min longer, therefore
(t+16) = time require by the 1st drain to empty the tank
let the emptied tank = 1
:
Each will do a fraction of draining and the two fractions = 1
:
+ = 1
multiply equation by t(t+16), cancel the denominators and we have
6(t+16) + 6t = t(t+16)
6t + 96 + 6t = t^2 + 16t
12t + 96 = t^2 + 16t
combine to form a quadratic equation on the right
0 = t^2 + 16t - 12t - 96
t^2 + 4t - 96 = 0
this factors to
(t+12)(t-8) = 0
the positive solution is what we want here
t = 8 min is the time of the 2nd drain
and
8+16 = 24 min is the time of the 1st drain
:
:
Check
=
reduce fractions
= 1
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