Scaling Water Bucket Capacity: A Simple Math Problem with Unexpected Insights
In this article, we will explore a mathematical problem related to scaling the capacity of water buckets to fill a tank. The problem presents an interesting real-world scenario and helps illustrate the concept of inverse proportionality in volume calculations. Let's dive in.
Problem Statement
Suppose it requires 30 buckets, each holding a certain amount of water, to fill a tank. If the capacity of each bucket is reduced to one-fifth of its original capacity, how many buckets are needed to fill the same tank?
Understanding the Concept
When the capacity of a bucket is reduced to one-fifth of its original capacity, each bucket can now hold only one-fifth of the amount of water it could hold before. This concept involves inverse proportionality in volume calculations. To understand the relationship, let's break down the steps:
Step 1: If the tank originally requires 30 buckets to be filled and each bucket now holds only one-fifth of its original capacity, we need to multiply the original number of buckets by 5.
Mathematically, if the original capacity of a bucket is C, and the new capacity is one-fifth of C, we can write:
Original number of buckets × Original capacity New number of buckets × New capacity
30 buckets × C New number of buckets × (C/5)
Solving for the new number of buckets:
New number of buckets 30 × 5 150 buckets
Concrete Example
To provide a more tangible example, let's assume the original capacity of each bucket is 100 liters. The total volume of water required to fill the tank is:
Total water to be filled in the tank 30 buckets × 100 liters/bucket 3000 liters
Now, if the capacity of each bucket is reduced to one-fifth of its original size (20 liters), the number of buckets required to fill the tank is:
No. of buckets required Total volume of the tank / New bucket capacity
No. of buckets required 3000 liters / 20 liters/bucket 150 buckets
General Formula and Application
A general formula for this problem is:
No.of buckets × bucket capacity constant
No.of buckets 20 Constant/ capacity
When capacity is reduced to 2/5 of its present capacity, the number of buckets required is:
No.of buckets required 150 buckets / (2/5) 150 × (5/2) 375/2 187.5 buckets
Conclusion
This analysis shows how a simple mathematical concept can be applied to solve real-world problems. It also highlights the importance of understanding inverse proportionality in volume calculations, which is useful in various fields such as engineering, construction, and environmental management.
Frequently Asked Questions (FAQs)
What is the relationship between the capacity of water buckets and the number of buckets needed to fill a tank?
The relationship is inverse. If the capacity of the buckets is reduced, the number of buckets required to fill the same volume increases proportionally.
Can you provide a real-world application of this concept?
This concept applies to various scenarios, such as filling water storage tanks in rural communities where resources are limited. Adjusting bucket sizes can help determine the optimal number of buckets needed to meet water demands efficiently.