One fill pipe A is 3 times faster than second fill pipe B...

One fill pipe $A$ is 3 times faster than second fill pipe $B$ and takes 32 minutes less than the fill pipe $B$. When will the cistern be full if both pipes are opened together?
(a) 28 mintues
(b) 24 minutes.
(c) 30 minutes
(d) Data inadequate.

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Key Concepts

Rate?Time Inverse Proportionality

This concept explains that the rate at which a task is performed (for example, filling a cistern) is the reciprocal of the time taken to complete it. If one worker or pipe works faster, it takes less time, and the relationship between speed and time is inversely proportional. Understanding this helps in translating comparative statements about speeds into mathematical equations relating time and work rate.

Proportional Reasoning in Work Problems

In problems where one agent is described as a multiple of another in terms of speed or efficiency (for example, one pipe being three times faster than another), proportional reasoning is used to relate their times and rates. This involves setting up ratios and equations that reflect the inverse relationship between speed and time, allowing one to solve for unknown quantities.

Addition of Rates (Combined Work Principle)

When two or more agents work together, their individual work rates add to give a total work rate. This principle is applied by adding the reciprocals of the individual times to complete the task, resulting in a combined rate which, when inverted, provides the total time to complete the task. This is crucial in solving problems involving simultaneous work, such as filling a cistern with multiple pipes.

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