Two pipes fill a reservoir. Working simultaneously, they fill it in 12 hours. One pipe is 10 hours faster than the other (i.e., it takes 10 fewer hours to fill the reservoir alone). How many hours does the faster pipe take to fill the reservoir.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Let the slower pipe take x hours. Then the faster takes (x − 10) hours. The combined rate equals 1/12 job/hour. Solve for x, then identify the faster pipe’s time. Given Data / Assumptions: Combined rate = 1/12 job/hour. Individual times: slower = x, faster = x − 10 (x > 10). Concept / Approach:Equation: 1/x + 1/(x − 10) = 1/12. Solve the quadratic for x, select the valid root, and compute x − 10. Step-by-Step Solution: 1/x + 1/(x − 10) = (2x − 10)/(x(x − 10)) = 1/12.12(2x − 10) = x(x − 10) ⇒ 24x − 120 = x^2 − 10x.x^2 − 34x + 120 = 0 ⇒ x = 30 or x = 4 (reject 4).Faster = x − 10 = 30 − 10 = 20 hours. Verification / Alternative check:Check: 1/30 + 1/20 = (2 + 3)/60 = 5/60 = 1/12; valid. Why Other Options Are Wrong:25/28/30/35 hours do not equal the correct 20-hour result. Hence “None of these.” Common Pitfalls:Picking the smaller (invalid) root x = 4 or forgetting that “faster” means fewer hours. Final Answer:None of these (correct time = 20 hours)

Two pipes fill a reservoir. Working simultaneously, they fill it in 12 hours. One pipe is 10 hours faster than the other (i.e., it takes 10 fewer hours to fill the reservoir alone). How many hours does the faster pipe take to fill the reservoir alone?

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