Question

314 weavers weaves 6594 shawls in \(\frac{1}{6}\) hours. What is the number of shawls weaved per hour by an average weaver? (a) 42 (b) 21 (c) 102 (d) 126

Short answer

Answer: An average weaver weaves 126 shawls per hour.

Step-by-step solution

Calculate shawls weaved per hour by all weavers

First, we need to find the total number of shawls weaved per hour by all weavers. We know that they weaved 6594 shawls in 1/6 hours. To find the number of shawls weaved in 1 hour, we will multiply the number of shawls weaved by the reciprocal of the fraction 1/6, which is 6. Total shawls per hour = 6594 shawls * 6 = 39564 shawls

Calculate the average shawls weaved per hour per weaver

Now that we have the total number of shawls weaved per hour (39564 shawls), we will divide this number by the total number of weavers (314) to find the average number of shawls weaved per hour per weaver. Average shawls per hour per weaver = 39564 shawls / 314 weavers = 126 shawls per weaver So, an average weaver weaves 126 shawls per hour, which corresponds to the option (d) 126.

Key concepts

Rate of Work in Word Problems

Rate of work problems often involve calculating how much of a task can be completed over a given period of time. These problems frequently arise in scenarios involving artisans, workers, or machines carrying out repetitive tasks.
The key to solving these problems is understanding the rate of work, which is typically expressed as a function of time. For example, if a team of workers can complete a specific task in a certain number of hours, their rate of work is the portion of the task completed in one hour.

• In the given problem, the rate for all weavers is calculated by determining the number of shawls woven per hour.
• This involves multiplying the total number of shawls by the reciprocal of the fractional time (i.e., multiplying by 6).
• Understanding the rate helps solve the problem by breaking it down into smaller, manageable sections.

Knowing how to find and use the rate of work allows you to tackle similar problems effectively.

Understanding Averages in Calculations

Averages are a common and simple concept that helps summarize data. In general, it defines a central value representing all the items in a set, making it easier to understand larger quantities.
When dealing with problems that involve many individuals or units completing a task, calculating the average work done per individual or unit can provide useful insights.

• For this shawl-weaving problem, once we know the total number of shawls woven per hour by all weavers, we calculate the average shawls woven per weaver per hour by dividing total shawls by the number of weavers.
• The result is an easily comprehensible figure (126 shawls per hour per weaver in this case).
• This average allows us to gauge the efficiency of each weaver within the group.

Hence, averages simplify the understanding of individual contributions to collective efforts.

Using Fractions in Work Calculations

Fractions are a crucial part of work calculations, particularly when not all tasks or times fit neatly into whole numbers. They help provide a more accurate representation of division in real-world scenarios.
In scenarios like the one given, fractional hours are common, signifying parts of an hour where work is being completed. Proper handling and conversion of these fractions are key to accurate results.

• Here, converting the fractional time (\(\frac{1}{6}\) hours) into a complete session (1 hour) is done by using the reciprocal (which is 6)
• This action involves multiplying the quantity of work (shawls) by 6 to find out how much work would be completed in one full hour.
• Proper usage of fractions ensures precise calculations and avoids errors that could misrepresent productivity or results.

Knowing when and how to apply fractions to work scenarios makes solving such problems more manageable.