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Chapter 43: Chapter 43

Problem 1228

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How long will it take Jones and Smith working together to plow a field which Jones can plow alone in 5 hours and Smith alone in 8 hours?

Short Answer

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Jones and Smith together can plow the field in \(\frac{40}{13}\) hours or approximately 3.08 hours.
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Determine work rates of Jones and Smith individually

To find the work rate of each person, we need to find the fraction of work done by each of them in one hour. For Jones, who finishes the job in 5 hours, the work rate is \(\frac{1}{5}\) (1 job per 5 hours) and for Smith, who completes the job in 8 hours, the work rate is \(\frac{1}{8}\) (1 job per 8 hours).

Step 2: Add the work rates of Jones and Smith

To find the work rate of both Jones and Smith working together, we need to add their individual work rates: \[\frac{1}{5} + \frac{1}{8} = \frac{8+5}{40} = \frac{13}{40}\] So, together they can do \(\frac{13}{40}\) of the job in one hour .

Step 3: Calculate the time taken by Jones and Smith working together

To determine the time it takes for Jones and Smith to finish the job together, divide 1 (the entire job) by their combined work rate: \[ \frac{1}{\frac{13}{40}} = \frac{1 * 40}{13} = \frac{40}{13}\] Therefore, it will take \(\frac{40}{13}\) hours or approximately 3.08 hours for Jones and Smith to plow the field together.

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