Wood Flooring

Date: 08/09/97 at 18:18:45
From: Paul Taylor
Subject: Production 

Estimating the number of linear feet in 1 sq. ft.
Making wood flooring, width is 3.25 inches.
Goal is to produce 5,000 sq. ft. per day.

Date: 08/10/97 at 03:07:57
From: Doctor Mike
Subject: Re: Production 

Hi Paul,  

Let me make sure I understand the question first.  
       ___________________________________________
      |                                           |
      |                                           |  3.25 in.
      |___________________________________________|
                          X ft.   

In this picture set-up, you want to know how many feet X is so that 
this board, which is X linear ft. long, will contain exactly ONE 
square foot of area. If that's not it, write back.
    
The way to do this is FIRST to figure what the area of the pictured 
board (above) actually is. You do that by multiplying the two 
dimensions together, but with the same length units. In inches, 
the dimensions are 3.25 and 12*X (12 times X). That makes the area 
3.25*12*X sq. in.  

SECOND we need to see that a square foot of area will have 144 square 
inches (12 times 12). With this we can set up an equation as follows: 

          3.25*12*X  =  144     or
                39*X = 144      or
          X = 144/39 = 48/13 = 3.6923 (approx.)

Since we now know that (48/13) linear ft. of 3.25 in. wide board is 
ONE sq. ft. in area, you take 5000 times that length to get 5000 sq. 
ft. of area. That is (48/13)*5000 = 18461.538 (approx.)

So, I guess your goal would be 18462 linear feet or 6154 linear yards 
per day.  Is that reasonable? 
   
You said something about estimating. With calculators around so much 
it is pretty easy to keep and use the conversion factor in its 48/13 
exact form instead of the decimal approximation. Just multiply the 
desired square footage by 48/13 to get linear footage. (That is, 
multiply square footage by 48 and divide that by 13.) Multiply actual 
linear footage by 13/48 to get square footage.   
   
I hope this helps.   
   
-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/