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Question
Hello:

If 20 men can paint 5 houses in 10 days, how many days can 40 men paint 15 houses?

If the rate of 20 men per 5 houses is used 20 men/5 houses What is the calculation for determining the answer? 20 men/5 houses is a rate of 4 men per 1 house or 4 men/1 house in 10 days. I think this now becomes 0.4 of a man men per house per day. Am I correct so far? I'm not sure what to do next to determine the answer.

I thank you for your assistance.

Following is the reason:

Yes, 0.4 man per house per day....but what is the question being asked?

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How do I use the above rate (0.4 man per house per day) to determine the answer?

Answer
Sorry, I did not notice the original question.  I need to revise my previous answer.

Let's look at from another point of view.
20 men can paint 5 houses in 10 days = 1 man can paint 5/20=1/4 of a house in 10 days
= 1 man can paint 1/40 of a house per day.  Thus, 40 men can paint 40(1/40)=1 house per day.

So, 40 men would need 15 days to paint 15 houses.

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

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Over 15 years teaching at the college level.

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NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

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B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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