Question

One carpenter can complete a kitchen in 8 days. With the help of another carpenter, they can do the job together in 4 days. How long would it take the second carpenter if he worked alone?

   One carpenter can complete a kitchen in 8 days. With the help of another carpenter, they can do the job together in 4 days. How long would it take the second carpenter if he worked alone?

Intermediate Algebra

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 5, Problem 66

Instant Answer

Solved by Expert Ankit Gupta

07/01/2020

Step 1

Step 1: Let's denote the time it takes for the second carpenter to complete the job alone as \(x\) days. Show more…

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One carpenter can complete a kitchen in 8 days. With the help of another carpenter, they can do the job together in 4 days. How long would it take the second carpenter if he worked alone?

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Key Concepts

Work Rate

This concept involves understanding that the rate at which a person completes a task is the fraction of the task done per unit time. If someone completes a task in a certain number of days, their work rate is the reciprocal of that time, representing the portion of the task finished per day.

Combined Work Rate

When multiple individuals work together on a task, their individual work rates are added to determine the total work rate. This combined rate represents the collective portion of the job that can be completed each day, enabling calculation of the total time required when working together.

Inverse Relationship Between Time and Rate

This principle states that the time required to complete a task is the reciprocal of the work rate. Once the work rate is known, determining the completion time involves taking its reciprocal, which is a central strategy in solving work-related problems.

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