Question 1208171
<pre>

Here is what I now believe is the best way to do this kind of problem, and how
to think it out,

I believe it should be taught this way:

I will use COMBINED VARIATION, defined as follows:
<i><b>
Combined variation describes a situation where a variable depends on two (or
more) other variables, and varies directly with some of them and varies
inversely with others (when the rest of the variables are held constant).</i></b>

We are asked for TIME REQUIRED, so let's see how TIME varies with each of the
other two variables, the number of workers and the number of jobs.

Time required varies DIRECTLY with the number of jobs IF the number of workers
remains constant. 
(The more jobs, the more time required. The less jobs, the less time required.
Obvious!) 

Time required varies INVERSELY with the number of workers IF the number of jobs
remains constant. (The more workers, the less time required.  The less workers,
the more time required. Obvious!) 

Therefore, when we let everything vary, we have a case of combined variation
So to state the combined variation involved:

<font size=5><b>Time required varies directly with the number of jobs
and inversely with the number of workers.</b></font>

Let T = time required, J = number of jobs, W = number of workers.

{{{T=k*expr(J/W)}}}

</pre>8 men take 12 days to assemble 16 machines<pre>

{{{12=k*expr(16/8)}}}

Solve for k:

{{{12=k*2}}}

{{{6=k}}}

Substitute 6 for k:

{{{T=6*expr(J/W)}}}

</pre>how many days will it take 15 men to assemble 50 machines?<pre>

{{{T=6*expr(50/15)}}}
  
{{{T=20}}}

answer: 20 days.

Edwin</pre>