You are here:

# Word Problems/Rates

Question
Hello:

Not too long ago, you responded to the following with this solution:

"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.

I still need further clarification so that I can understand this type of solution.

Can you use the same type of complete calculation as you used above to determine the answers to the following?

20 men can paint 5 houses in 10 days. In 8 days how many men can paint men 2 houses?

Use the complete calculation as you used above!

20 men can paint 5 houses in 10 days. In 8 days, 10 men to paint how many houses?

Once again use the complete calculation to determine the answers!

"20 workers can paint 5 houses in 10 days."
20 workers × 10 days = 200 worker-days
(200 worker-days)/(5 houses) = (40 worker-days)/house

2 houses × (40 worker-days)/house = 80 worker-days
(80 worker-days)/(8 days) = 10 workers

In 8 days, 10 workers can paint 2 houses.
:::::
"20 workers can paint 5 houses in 10 days."
20 workers × 10 days = 200 worker-days
(200 worker-days)/(5 houses) = (40 worker-days)/house

10 workers × 8 days = 80 worker-days
80 worker-days × (1 house)/(40 worker-days) = 2 houses
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment No Comment

Word Problems

Volunteer

#### Janet Yang

##### Expertise

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.

##### Experience

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

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

Education/Credentials
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.

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