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Gardening. Nicole can weed her vegetable garden in 50 min. Glen can weed the same garden in 40 min. How long would it take if they worked together?

Gardening. Nicole can weed her vegetable garden in 50 min. Glen can weed the same garden in 40 min. How long would it take if they worked together?

Algebra and Trigonometry (6th Edition)
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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**Gardening Problem:** Nicole can weed her vegetable garden in 50 minutes. Glen can weed the same garden in 40 minutes. How long would it take if they worked together? **Explanation:** To solve this, we can use the concept of work rates. Nicole's rate is 1 garden per 50 minutes, and Glen's rate is 1 garden per 40 minutes. To find out how long it will take them together, we add their rates: Nicole's rate: \( \frac{1}{50} \) garden per minute Glen's rate: \( \frac{1}{40} \) garden per minute Combined rate: \( \frac{1}{50} + \frac{1}{40} \) To add these fractions, find a common denominator, which is 200. Then: \[ \frac{4}{200} + \frac{5}{200} = \frac{9}{200} \] So together, they can weed \(\frac{9}{200}\) of the garden per minute. To find out how long it takes to weed the whole garden: \[ \text{Time} = \frac{1}{\left(\frac{9}{200}\right)} = \frac{200}{9} \] This is approximately 22.22 minutes. Therefore, if Nicole and Glen work together, it will take them about 22 minutes to weed the garden.
Transcribed Image Text:**Gardening Problem:** Nicole can weed her vegetable garden in 50 minutes. Glen can weed the same garden in 40 minutes. How long would it take if they worked together? **Explanation:** To solve this, we can use the concept of work rates. Nicole's rate is 1 garden per 50 minutes, and Glen's rate is 1 garden per 40 minutes. To find out how long it will take them together, we add their rates: Nicole's rate: \( \frac{1}{50} \) garden per minute Glen's rate: \( \frac{1}{40} \) garden per minute Combined rate: \( \frac{1}{50} + \frac{1}{40} \) To add these fractions, find a common denominator, which is 200. Then: \[ \frac{4}{200} + \frac{5}{200} = \frac{9}{200} \] So together, they can weed \(\frac{9}{200}\) of the garden per minute. To find out how long it takes to weed the whole garden: \[ \text{Time} = \frac{1}{\left(\frac{9}{200}\right)} = \frac{200}{9} \] This is approximately 22.22 minutes. Therefore, if Nicole and Glen work together, it will take them about 22 minutes to weed the garden.
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