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# Word Problems/Inverse Proportions

Question
Hello:

20 men build a house in 6-days.
If the men are increased to 30 men, then they take 4-days to build the same house--1 1/2 of 20 men equals 30 men.  The inverse of 1 1/2 is 2/3 so 2/3 of 6 days is 4 days.

If number of hours per day is added as in 20 men can build a hours in 6 days working 8 hours a day, 30 men and build the same house working how many days and how many hours per day?

When there are two quantities, the inverse proportions are not too difficult. But I do not know what to do with the number of hours worked per day, a third quantity.  Is it 2/3 of 8 hours per day just as it is 2/3 of 6 days?

If the hours worked per day was 8, that would be 1/3 of a day that was worked.
If the hours were increased to 12, that would be and increase to 1/2 a day.

Since we went from 8 to 12, we increased by 12/8, which  is 3/2.
This is inversely proportional to the number of days worked.

In theory, ignoring the fact that people start to work slower after working 8 hours,
that means the total days would be decreased by 2/3.

Basically, the number of days and the number of hours are both measurements of time.
The number of hours worked per day is inversely proportional to the number of days worked,
for as hours go up, the number of required days goes down.

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Word Problems

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#### Scott A Wilson

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