Mats Production Rate Calculation: A Comprehensive Guide

In this article, we will explore the methods used to calculate work rates when multiple individuals, such as men and boys, are involved in producing a specific number of mats. We'll delve into the logical steps and rationale behind these calculations to ensure clarity and accuracy in your work rate analysis.

Problem Statement and Solution

Let's begin by examining a typical problem where we are given that 10 men or 30 boys can make 390 mats in 20 days. The problem then asks, 'How many mats will be made by 8 men and 15 boys in 20 days?' Let's break it down step-by-step.

Step-by-Step Calculation

First, let's define the variables:

X: Number of mats made by 1 man in 1 day. Y: Number of mats made by 1 boy in 1 day.

From the problem, we know two key equations:

10 men can make 390 mats in 20 days:

120 390

30 boys can make 390 mats in 20 days:

30Y20 390

We can solve for X and Y:

Multiply the first equation by 4/5:

8X20 312

Multiply the second equation by 1/2:

15Y20 195

Finally, summing the results:

8X 15Y20 312 195 507 mats

Understanding Man-Days and Boy-Days

In many work rate problems, the term 'man-day' (or 'boy-day') is used to represent the amount of work done by one person in one day. For instance, in the previous problem, a 'man-day' represents the work done by 1 man in 1 day. Consequently, 'boy-days' represent the work done by 1 boy in 1 day.

Example 1: 10 Men and 30 Boys Producing Mats

Given that 10 men or 30 boys can make 390 mats in 20 days, we can calculate the work rate for each group and then combine their efforts for the final calculation.

Calculation Details

120 390 rarr; X 390 / (1020) 1.95 mats per man-day 30Y20 390 rarr; Y 390 / (3020) 0.65 mats per boy-day

For 8 men and 15 boys over 20 days:

8 men: 81.9520 156 mats 15 boys: 150.6520 49.5 mats

Combining the efforts: 156 49.5 205.5 mats

Example 2: 8 Men and 4 Boys Producing Mats

Now let's look at another problem where we need to calculate the number of mats produced by 8 men and 4 boys in 20 days.

Calculation Details

20 men-days: 201.3 26 mats 8 men: 81.320 208 mats 40 boys-days: 41.320 52 mats 4 boys: 40.6520 52 mats

Combining the efforts: 208 52 260 mats

Conclusion and Final Answer

Based on the given problem, the combined effort of 8 men and 4 boys will produce 260 mats in 20 days. This conclusion is based on the work rate of each individual and combining their efforts over the given period.

Key Takeaway: Always break down the problem into smaller components and calculate the work rate for each individual or group. Then, sum the efforts to find the total production rate.