Inversely & Directly Proportional

[KWF]

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?


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

 

[Deleted member 4993]

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?


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

What are your thoughts?

 

[KWF]

What are your thoughts?

Well, my thoughts are confused!

 

[JeffM]

Well, my thoughts are confused!

LOL Let's help unconfuse you.

Two variable, x and y are said to be directly proportional if and only if

\(\displaystyle there\ exists\ a\ number\ k > 0\ such\ that\ x = k * y.\) Informally speaking, x and y go up together or down together.

Two variable, x and y are said to be inversely proportional if and only if

\(\displaystyle there\ exists\ a\ number\ k > 0\ such\ that\ x = k * \dfrac{1}{y}.\) Informally speaking, x and y go in different directions.

Do you get the concepts?

What are the three variables in your problem? In a word problem, the very first thing to do ALWAYS is to identify the relevant variables or unknowns and write them down along with a letter to stand for each one. To get you started, I'll show you how to do it for one variable.

L = length in hours of the working day.

What are the other two?

 

[KWF]

LOL Let's help unconfuse you.

Two variable, x and y are said to be directly proportional if and only if

\(\displaystyle there\ exists\ a\ number\ k > 0\ such\ that\ x = k * y.\) Informally speaking, x and y go up together or down together.

Two variable, x and y are said to be inversely proportional if and only if

\(\displaystyle there\ exists\ a\ number\ k > 0\ such\ that\ x = k * \dfrac{1}{y}.\) Informally speaking, x and y go in different directions.

Do you get the concepts?

What are the three variables in your problem? In a word problem, the very first thing to do ALWAYS is to identify the relevant variables or unknowns and write them down along with a letter to stand for each one. To get you started, I'll show you how to do it for one variable.

L = length in hours of the working day.

What are the other two?

I'm only guessing, but I' ll say number of days worked, and length of the wall. (?) I only know that then one unit goes up another goes down (inverse); when both units increase or decrease the same (direct), I think with the same proportion, but I cannot clearly explain or undersand this idea. I try to understand mathematics but my brain refuses to understand

 

[Deleted member 4993]

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?


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

In your case there are three variables:

Men

Length of wall

Time (days*hours worked)

Number of men needed will be inversely proportional to time - if you keep length of wall constant.

What else....

 

[KWF]

In your case there are three variables:

Men

Length of wall

Time (days*hours worked)

Number of men needed will be inversely proportional to time - if you keep length of wall constant.

What else....

That's all for now... thanks for everyone's help!