Filling Time Calculation for Pipes: A Comparative Analysis

In many real-world scenarios, understanding the relationship between the number of pipes and the time required to fill a water tank is crucial. This article explores the scenario where 6 pipes can fill a tank in 1 hour and 20 minutes, and then determines how long it would take for 5 pipes to accomplish the same task. Additionally, it delves into the concept of indirect proportion and its implications.

Understanding the Problem

The problem at hand involves calculating the time it takes for 5 pipes to fill a water tank, given that 6 pipes can do so in 1 hour and 20 minutes.

Step-by-Step Solution

Step 1: Convert the time to minutes. Step 2: Find the rate at which the tank is filled by 6 pipes. Step 3: Find the time it takes for 5 pipes to fill the tank. Step 4: Convert the time to minutes.

Solution Walkthrough

Given:

6 pipes can fill the tank in 1 hour and 20 minutes.

Step 1: Convert the time to minutes.

1 hour and 20 minutes 1 × 60 minutes 20 minutes 80 minutes.

Step 2: Find the rate at which the tank is filled by 6 pipes.

Rate Total volume of the tank / Time taken to fill the tank Rate 1 / (80/60) tanks per hour 0.75 tanks per hour.

Step 3: Find the time it takes for 5 pipes to fill the tank.

Rate of 5 pipes 0.75 tanks per hour × (5/6) 0.625 tanks per hour.

Time taken 1 tank / 0.625 tanks per hour 1.6 hours.

Step 4: Convert the time to minutes.

1.6 hours 1.6 × 60 minutes 96 minutes.

Therefore, it will take 96 minutes for 5 pipes to fill the tank.

Concept of Indirect Proportion

This is a classic problem involving the concept of indirect proportion. The number of pipes required to fill the tank and the time taken to fill them are inversely proportional. This means that the more pipes you have, the less time it will take to fill the tank, and vice versa.

Additional Considerations

The above solution assumes that each pipe is of the same size and operates at full capacity. However, practical scenarios often differ due to various factors:

If the pipes are not running at full capacity, the time might be the same or slightly more. If the pressure on the source side is fixed, you would likely get more throughput through the remaining 5 pipes, but the exact number depends on the specific conditions such as pipe size, the number of bends, and overall resistance. Increasing the pressure might not always lead to more throughput per pipe, and in some cases, it might even decrease it.

Therefore, the correct answer is “most likely somewhere between 80 and 96 minutes.”

Conclusion

Understanding the relationship between the number of pipes and the time required to fill a water tank is essential in many fields, including engineering, plumbing, and industrial processes. The key to solving this problem lies in the concept of indirect proportion, and practical considerations can affect the actual filling time.