If two function simultaneously, the reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?

25 hours
28 hours
30 hours
35 hours

Correct Answer: 30 hours

Explanation:

Suppose that one pipe takes N hours to fill the reservoir. Then another pipe takes (N - 10) hours.
∴ 1/N + 1/(N - 10) = 1/12
⇒ 12(N - 10 + N) = N(N - 10)
or N² - 34N + 120 = 0
or (N - 30)(N - 4) = 0
∴ N = 30 or N = 4
So, the faster pipe takes 30 hours to fill the reservoir.

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