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# Number Theory/Rates

Question
Hello:

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

20 men/5 houses is a rate of 4 men per 1 house or 4 men/1 house in 10 days.  This now becomes 0.4 of man men per house per day.  I'm not sure what to do next to determine the answer.

I think I have been over this with you before.
The number of houses is jointly proportional to the number of men and the number of days.
So h = kmd.  Substituting the given gets you to k = 1/40.  So h = md/40 and d = 40h/m.  When m=40 and h =15, d =15.
Best wishes

vijilant

Number Theory

Volunteer

#### Vijilant

##### Expertise

Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

##### Experience

Teacher of math for 53 years

Organizations
AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley

Publications
Journal of mathematics and its applications M500 magazine

Education/Credentials
BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

Awards and Honors
State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 £50 prize First class honours in OU BA Mathematics

Past/Present Clients
I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.