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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: 33 men

I thank you for your reply.

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

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