Word Problems/Unit Rates

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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 my arithmetic is correct, here is the unit rate from the first part of the question:
(5 houses/20 men)/(10 days/1) = 2 1/2 houses per man per day

How would I use this rate to determine the answer by using 40 men and 15 houses?

I thank you for your reply!

Answer
5 houses by 20 men, gives a rate of 5/20 = 1/4 of a house per man in 10 days.
Thus, per day it is (1/4)/10 or 1/40 of a house per man per day.

So, 40 men work at the rate of 40(1/40) house per day = 1 house per day.

Therefore, 15 days would be needed.

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Volunteer


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!

Experience

Over 15 years teaching at the college level.

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

Education/Credentials
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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