How would I solve this **Problem: Calculating Combined Work Time***Scenario*Suppose that a lawn can be raked by one gardener in 5 hours and by a second gardener in 4 hours. The question is: How long will it take for the two gardeners to rake the lawn working together?*Solution Approach*When two or more people are working together to complete a task, we can add their rates of work to find the total time required to complete the task.1. **Gardener 1's Rate:** One garden in 5 hours → Work rate = $ \frac{1}{5} $ of the garden per hour.2. **Gardener 2's Rate:** One garden in 4 hours → Work rate = $ \frac{1}{4} $ of the garden per hour.3. **Combined Rate:** Combined work rate = $ \frac{1}{5} + \frac{1}{4} $ To calculate, find a common denominator (20): \[ \frac{1}{5} = \frac{4}{20} \\ \frac{1}{4} = \frac{5}{20} \\ \] Add the rates: \[ \frac{4}{20} + \frac{5}{20} = \frac{9}{20} \]4. **Total Time:** To find the time, take the reciprocal of the combined rate: \[ \text{Time} = \frac{20}{9} \approx 2.22 \]*Solution*Working together, the two gardeners can rake the garden in about 2.22 hours. (Round to two decimal places as needed.)*Answer Box:* Enter your answer in the box.

One gardener can make the lawn in 5 hours Another gardener can make the lawn in 4 hours

Answered: Suppose that a lawn can be raked by one…

Suppose that a lawn can be raked by one gardener in 5 hours and by a second gardener in 4 hours. How long it will take the two gardeners to rake the lawn working ogether? Norking togethor

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Equations and inequalities describe the relationship between two mathematical expressions.

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Question

How would I solve this

**Problem: Calculating Combined Work Time**

*Scenario*

Suppose that a lawn can be raked by one gardener in 5 hours and by a second gardener in 4 hours. The question is: How long will it take for the two gardeners to rake the lawn working together?

*Solution Approach*

When two or more people are working together to complete a task, we can add their rates of work to find the total time required to complete the task.

1. **Gardener 1's Rate:**
One garden in 5 hours → Work rate = $ \frac{1}{5} $ of the garden per hour.

2. **Gardener 2's Rate:**
One garden in 4 hours → Work rate = $ \frac{1}{4} $ of the garden per hour.

3. **Combined Rate:**
Combined work rate = $ \frac{1}{5} + \frac{1}{4} $

To calculate, find a common denominator (20):
\[
\frac{1}{5} = \frac{4}{20} \\
\frac{1}{4} = \frac{5}{20} \\
\]

Add the rates:
\[
\frac{4}{20} + \frac{5}{20} = \frac{9}{20}
\]

4. **Total Time:**
To find the time, take the reciprocal of the combined rate:
\[
\text{Time} = \frac{20}{9} \approx 2.22
\]

*Solution*

Working together, the two gardeners can rake the garden in about 2.22 hours. (Round to two decimal places as needed.)

*Answer Box:* Enter your answer in the box.

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