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Word Problems/Compound Proportions



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 ----------


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)  

men vs. wall
wall vs. days
wall vs. hours

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

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Scott A Wilson


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