Word Problems/Unit Rates

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Question
Hello:

How is the following changed to a unit rate?

20 men can paint 5 houses in 10 days.

Is it men per house per day; house per day per man; days per house per man, etc.?

I thank you for your reply.

Answer
Depends on the phrasing of the question, i.e., what you're trying to solve for.
Without seeing the question, I'm guessing you need to determine how long it would take a certain number of men to paint a specified number of houses. In that case, you want to know the number of man-days it takes to paint one house.

For example, "20 men can paint 5 houses in 10 days. How long will it take 10 men to paint 2 houses?"
(20 men 10 days) / (5 houses) = (200 man-days) / (5 houses) = (40 man-days)/house
2 houses (40 man-days)/house = 80 man-days
80 man-days 10 men = 8 days
It takes 10 men 8 days to paint 2 houses.

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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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