SOLUTION: If it takes 20 people to complete as task in 12 days. How many people will it take to complete the task in 8 days?

We have two quantities, the number of people and the number of days.
We first have to decide whether the two quantities are DIRECTLY
proportional or INVERSELY proportional:

The fraction on the left will contain one quantity "before" and "after",
and the fraction on the right will contain the other quantity "before"
and after.

Direct variation:

When one quantity is INcreased the other quantity is also INcreased, and when
one quantity is DEcreased to other quantity is also DEcreased.

If that is the case, then we use this
proportion:



Inverse variation:

When one quantity is increased the other quantity is decreased, and when one
quantity is decreased the other quantity is increased.

If that is the case, then we have INVERSE variation, and so we must INVERT the
second ratio above.



We have to decide whether PEOPLE and DAYS are DIRECTLY or
INVERSELY proprotional.  So we ask which of these is true:

1. DIRECTLY{  The MORE people we have working, the MORE days it will take and
the FEWER people we have working, the FEWER days it will take them.

or

2. INVERSELY: The MORE people we have working, the FEWER days it will take and
The FEWER people we have working, the MORE days it will take them.


Obviously 1 is false and 2 is true

So they are NOT directly proportional so this proportion does not work: 



Since the quatities people and days are INVERSELY proportional we INVERT 
the second ratio and we have this instead:




People in 1st situation = 20
People in second situation = ????  (Let that be N people)
Days in 1st situation = 12
Days in second situation = 8

 = 

8N = 240
 N = 30

So it will take 30 people to complete the task in 8 days.

Edwin