If a single inlet pipe can fill a tank in 6 hours, what fraction of the tank will be filled by this pipe in 1 hour?

Introduction / Context:When a job takes T hours, the constant rate per hour is the reciprocal, 1/T of the job per hour. Pipes-and-cistern questions frequently ask for the fraction filled in a given time.

Given Data / Assumptions:

• The pipe fills the entire tank in 6 hours.
• Filling rate is constant (no leakage or pressure fluctuations).
• We seek the portion filled in exactly 1 hour.

Concept / Approach:Rate = work/time. For one full tank in 6 hours, the per-hour fraction filled is 1/6 of the tank.

Step-by-Step Solution:Total work (one full tank) = 1 tank.Time to complete = 6 hours.Rate = 1 / 6 tank per hour.Portion filled in 1 hour = rate * time = (1/6) * 1 = 1/6.

Verification / Alternative check:In 6 hours at 1/6 per hour, total filled = 6 * (1/6) = 1 tank, consistent.

Why Other Options Are Wrong:1/3 and 1/4 imply faster filling; 1/5 is arbitrary relative to the given 6-hour completion.

Common Pitfalls:Confusing rate with remaining fraction or trying to proportion time and fraction incorrectly.

Final Answer:1/6