Word Problems/Unit Rates



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.

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


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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