Calculating Tank Filling Time with Two Taps: A Comprehensive Guide

The efficiency of a system can be significantly impacted by the combination of its components. When two taps or pipes are used to fill a tank, understanding how their combined performance affects the filling time is crucial. In this article, we will explore a common scenario where the filling time of a tank is determined using two taps, each with a known individual filling rate.

Understanding the Problem

To start, let us consider the problem of determining how long it will take two taps to fill a tank if one tap can fill the tank in 6 hours and the other in 4 hours. This question requires an understanding of the individual rates of each tap and how these rates combine to affect the filling process.

Calculating Individual Rates

The first step is to determine the filling rate of each tap. The filling rate is the portion of the tank that each tap can fill in one hour.

Tap A:
In 6 hours, Tap A can fill the entire tank. Therefore, the filling rate of Tap A is:

Rate of Tap A 1/6 of the tank per hour.

Tap B:
In 4 hours, Tap B can fill the entire tank. Therefore, the filling rate of Tap B is:

Rate of Tap B 1/4 of the tank per hour.

Combining the Rates

To find the combined rate of the two taps, we add their individual rates. However, for this addition to be possible, the denominators must be the same. To achieve this, we find the least common multiple (LCM) of the denominators, which in this case is 12.

Filling rate of Tap A 1/6 2/12 of the tank per hour

Filling rate of Tap B 1/4 3/12 of the tank per hour

Combined rate 2/12 3/12 5/12 of the tank per hour

Calculating the Filling Time

Now that we have the combined rate of both taps, we can determine the time required to fill the entire tank. The formula to calculate the time is:

Time 1 / (combined rate)

Time 1 / (5/12) 12/5 2.4 hours.

Converting 12/5 hours into hours and minutes:

2.4 hours 2 hours and 0.4 * 60 24 minutes.

Therefore, the two taps together will fill the tank in 2 hours and 24 minutes.

Additional Considerations

It is important to note that in a real-world scenario, the size of the tank and the amount of water flowing from each tap are not specified. If we assume the tank’s capacity is X liters, we can still work with the rates:

Rate of Tap A X/6 liters per hour

Rate of Tap B X/4 liters per hour

The combined rate for both taps is:

X/6 X/4 2X/12 3X/12 5X/12 liters per hour

Since we need to fill only one tank, the time taken is:

Time X / (5X/12) 12/5 hours 2.4 hours 2 hours and 24 minutes.

Conclusion

In summary, the time required for two taps to fill a tank is determined by their individual filling rates. By adding these rates, we can find the combined time needed to fill the tank. The example given shows how two taps, one filling in 6 hours and the other in 4 hours, will fill the tank in 2 hours and 24 minutes. Understanding these calculations can be useful in various fields, such as plumbing, water management, and industrial liquid processing.

The key takeaway is that combining the rates of multiple taps can provide a clear insight into the total filling time, making it easier to manage and optimize water flow in practical applications.