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Word Problems/Unit Rates & Proportions

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Question
Hello:

How is the solution found for the following by using the unit rate method?


If 6 men can finish a job in 10 hours, 12 men can finish the same job in how many hours?

6 men/10 hours X 12 men or 10 hours/6 men X 12 men will not produce the correct answer.

I thank you for your reply.

Answer
6 workers complete a job in 10 hours.

1 worker does ⅙ of the job in 10 hours.
⅙ job/(10 hours) = ⅙10 job/hour = 1/60 job/hour
1 worker does 1/60 of the job per hour.

12 workers (1/60 job)/(worker-hour) = ⅕ job/hour
12 workers complete ⅕ of the job per hour.

1 job (⅕ job)/hour = 5 hours
It takes the 12 workers 5 hours to perform the job.

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Janet Yang

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Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language.

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I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley, and a Master of Business Administration degree from The Wharton School.

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George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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