Rice Consumption Rate and Calculation of Time Required

Understanding the consumption rate of a staple food like rice is crucial in many practical scenarios, such as managing food supplies for households, communities, or even larger organizations. This article delves into the calculation of how many days it takes for a specific number of people to consume a certain amount of rice, based on a given scenario.

Let's explore the following problem: 40 people consume 200 kg of rice in 30 days. How many days will 30 people take to consume 500 kg of rice?

Setting Up the Problem

This scenario can be formulated as a ratio problem. We need to set up the relationship between the number of people, the amount of rice, and the duration to find the answer.

Ratio of Consumption

First, we calculate the daily consumption rate per person:

[text{Daily consumption per person} frac{200 , text{kg} , text{rice}}{40 , text{people} times 30 , text{days}}]

Calculation Steps

We can break down the equation to simplify it:

[frac{200 , text{kg} , text{rice}}{40 , text{people} times 30 , text{days}} frac{500 , text{kg} , text{rice}}{30 , text{people} times x , text{days}}]

Simplifying the Problem

By dividing both the numerator and the denominator of the left-hand side by their common factors, we get:

[frac{200 div 10 div 10}{40 div 10 times 30 div 10} frac{500 div 10}{3 div 10}]

This simplification gives:

[frac{2}{4 times 3} frac{50}{3x}]

Further simplification:

[frac{2 div 2}{4 div 2 times 3 div 3} times frac{3 div 3}{1} frac{50}{x}] [frac{1}{2} times 3 frac{50}{x}]

[frac{3}{2} frac{50}{x}]

Solving for (x):

[x frac{50 times 2}{3} 100 , text{days}]

Verification of Calculation

Let's verify the calculation using the alternative methods:

1. Using the direct consumption rate:

[text{Daily consumption by 40 people} frac{200 , text{kg}}{30 , text{days}} approx 6.67 , text{kg/day}] [text{Daily consumption by 1 person} frac{6.67 , text{kg/day}}{40 , text{people}} approx 0.1667 , text{kg/day/person}] [text{Daily consumption by 30 people} 0.1667 , text{kg/day/person} times 30 , text{people} approx 5 , text{kg/day}] [text{Days needed for 30 people to consume 500 kg} frac{500 , text{kg}}{5 , text{kg/day}} 100 , text{days}]

2. Using the simple method:

[text{Daily consumption by 1 person} frac{200 , text{kg}}{40 , text{people} times 30 , text{days}} approx 0.1667 , text{kg/day/person}] [text{Daily consumption by 30 people} 0.1667 , text{kg/day/person} times 30 , text{people} approx 5 , text{kg/day}] [text{Days needed for 30 people to consume 500 kg} frac{500 , text{kg}}{5 , text{kg/day}} 100 , text{days}]

3. Using the proportion method:

[text{Daily consumption by 30 people} frac{500 , text{kg}}{3000 , text{people/days}} approx 0.1667 , text{kg/day/person}] [text{Days needed for 30 people to consume 500 kg} frac{500 , text{kg}}{0.1667 , text{kg/day}} 100 , text{days}]

Conclusion

The calculated result is consistent with all the methods used. Therefore, it will take 30 people 100 days to consume 500 kg of rice.