Question

Working Together Suppose that a lawn can be raked by one gardener in 3 hours and by a second gardener in 5 hours. (a) Mentally estimate how long it will take the two gardeners to rake the lawn working together. (b) Solve part (a) symbolically.

Name: Problem 101, Chapter 2: College Algebra with Modeling and Visualization
Uploaded: 2021-04-20T11:04:09-08:00
Duration: 4 min 27 s
Channel: Ruby P
Description: Working Together Suppose that a lawn can be raked by one gardener in 3 hours and by a second gardener in 5 hours. (a) Mentally estimate how long it will take the two gardeners to rake the lawn working together. (b) Solve part (a) symbolically.

   Working Together Suppose that a lawn can be raked by one gardener in 3 hours and by a second gardener in
5 hours.
(a) Mentally estimate how long it will take the two gardeners to rake the lawn working together.
(b) Solve part (a) symbolically.

College Algebra with Modeling and Visualization

Gary K. Rockswold 4th Edition

Chapter 2, Problem 101

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Solved by Expert Ruby P

04/20/2021

Step 1

The first gardener can rake 1/3 of the lawn in one hour, and the second gardener can rake 1/5 of the lawn in one hour. Show more…

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Working Together Suppose that a lawn can be raked by one gardener in 3 hours and by a second gardener in 5 hours. (a) Mentally estimate how long it will take the two gardeners to rake the lawn working together. (b) Solve part (a) symbolically.

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Key Concepts

Work Rate

A work rate represents the amount of work completed per unit time. In this context, if a gardener can finish the entire lawn in a specific number of hours, then their work rate is the fraction of the lawn they can rake per hour, typically calculated as 1 divided by the number of hours it takes.

Combined Work Rate

When multiple agents work together, their individual work rates add up to form a combined work rate. This principle allows us to determine the total time required to complete a task by summing the contributions of each worker and then taking the reciprocal of this sum.

Algebraic Problem Solving in Work Problems

Solving work problems symbolically involves setting up equations that equate the sum of individual work rates to the combined work rate. This method often includes finding a common denominator, simplifying the resulting expression, and solving for the total time required to complete the task when all agents work together.

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