SOLUTION: A tank has 2 inlet taps A & B & 1 outlet tap C. From tap A tank gets filled in 15min. & from tap B tank gets filled in 25 min. Tank got empty when tap C is opened in 30 min. If ta

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A tank has 2 inlet taps A & B & 1 outlet tap C. From tap A tank gets filled in 15min. & from tap B tank gets filled in 25 min. Tank got empty when tap C is opened in 30 min. If ta      Log On


   

Question 856970: A tank has 2 inlet taps A & B & 1 outlet tap C. From tap A tank gets filled in 15min. & from tap B tank gets filled in 25 min. Tank got empty when tap C is opened in 30 min. If tap C is opened after 7 min. of tap A&B, then find out the time that the tank gets fully filled.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A tank has 2 inlet taps A & B & 1 outlet tap C.
From tap A tank gets filled in 15 min. & from tap B tank gets filled in 25 min.
Tank got empty when tap C is opened in 30 min.
If tap C is opened after 7 min. of tap A&B, then find out the time that the tank gets fully filled.
:
Let t = total time to fill the tank under these conditions Taps A&B on
(t-7) = time that tap C was on
:
Let the completed job = 1 (a full tank)
:
A and B add water, tap C subtracts water
t%2F15 + t%2F25 - %28%28t-7%29%29%2F30 = 1
multiply by 150 to cancel the denominators, resulting in:
10t + 6t - 5(t-7) = 150
16t - 5t + 35 = 150
11t = 150 - 35
11t = 115
t = 115/11
t = 10.45 minutes to fill the tank
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You can confirm this for yourself, substitute 10.45 for t in the original equation, see if it = 1 or very close to 1
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