Question
Pipe A fills a tank in 12 h; Pipe B in 15 h; Pipe C
empties it in 10 h. All three opened together. After x hours, C is closed and tank gets full in 2 more hours. Find x.Solution
ATQ,
Rates: A=1/12, B=1/15, C=−1/10.
Net with C: 1/12 + 1/15 − 1/10 = (5 + 4 − 6)/60 = 3/60 = 1/20. Without C: 1/12 + 1/15 = (5 + 4)/60 = 9/60 = 3/20. Let x hours at 1/20, then 2 hours at 3/20 equals 1 tank. x·(1/20) + 2·(3/20) = 1 ⇒ x/20 + 6/20 = 1 ⇒ x/20 = 14/20 ⇒ x = 14. Answer: 14 hours.
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