Question

An old computer can do the weekly payroll in 5 hours. A newer computer can do the same payroll in 3 hours. The old computer starts on the payroll, and after 1 hour the newer computer is brought on-line to work with the older computer until the job is finished. How long will it take both computers working together to finish the job? (Assume the computers operate independently.)

Name: Problem 75, Chapter 1: Precalculus
Uploaded: 2021-07-29T12:01:18-08:00
Duration: 3 min 23 s
Channel: Yujie Wang
Description: An old computer can do the weekly payroll in 5 hours. A newer computer can do the same payroll in 3 hours. The old computer starts on the payroll, and after 1 hour the newer computer is brought on-line to work with the older computer until the job is finished. How long will it take both computers working together to finish the job? (Assume the computers operate independently.)

   An old computer can do the weekly payroll in 5 hours. A newer computer can do the same payroll in 3 hours. The old computer starts on the payroll, and after 1 hour the newer computer is brought on-line to work with the older computer until the job is finished. How long will it take both computers working together to finish the job? (Assume the computers operate independently.)

Precalculus

Raymond A. Barnett,… 7th Edition

Chapter 1, Problem 75

Instant Answer

Solved by Expert Yujie Wang

07/29/2021

Step 1

The speed of the old computer is $V_O = \frac{P}{5}$, which means the old computer can process $\frac{P}{5}$ payrolls in one hour. Similarly, the speed of the new computer is $V_N = \frac{P}{3}$, which means the new computer can process $\frac{P}{3}$ payrolls in Show more…

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An old computer can do the weekly payroll in 5 hours. A newer computer can do the same payroll in 3 hours. The old computer starts on the payroll, and after 1 hour the newer computer is brought on-line to work with the older computer until the job is finished. How long will it take both computers working together to finish the job? (Assume the computers operate independently.)

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Key Concepts

Fraction of Task Completed

This concept involves determining how much of a task has been completed after a certain period. It is crucial for understanding the remaining work and for setting up equations that relate portions of work to time.

Work Rate

This concept refers to the measure of work completed per unit time. It is essential for determining how long an individual or machine takes to finish a task by calculating the fraction of the job done in one unit of time.

Combined Work

This concept addresses scenarios where multiple agents are working simultaneously on a task. Their individual work rates can be added together to find the total rate at which the work is completed, allowing for calculation of the time required to finish the task when working together.

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