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# Word Problems/Compound Proportions

Question
QUESTION: Hello:

How is the answer to the following determined?

6 men can build a wall 96 feet long in 18 days when the day is 11 hours long; how many men must be employed to build 64 feet of wall in 2 days when the day is 12 hours long?

ANSWER: If 6 men can build 96 feet in 18 days, then take 96/6 = 16 feet,
and that is the amount one man can build in 18 days.

Since that is 16 feet in 18 days, that is 16/18 of a foot per day,
and that is 8/9.  That means 1 man builds 8/9 of of a foot of wall per day.

Now there are 11 hours in one of those day, which means that one man can build 8/99 per hour.

To build 64 feet of wall in 2 12-hour days means each man has 24 hours.

For one man, it was determined that 8/99 could be produced an hour.
In 24 hours, it would be 24*8/99 = 8*8/33 = 64/33 feet.
That is how much wall could be done by one man in 24 hours.

To get all 64 feet done, it would take 33 men since 33(64/33) = 64 feet.

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you or the great reply.  I do have this follow-up question:

Which units from the above are inversely proportional and which units are directly proportional and why?

variables: men (number of), wall (feet of), days (number of), hours (number per day)

proportional
------------
men vs. wall
wall vs. days
wall vs. hours

inversely proportional
----------------------
men vs. days
men vs. hours
days vs. hours

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the reply and information!

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#### Scott A Wilson

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