Question 1207697
If 3 people can paint 2 rooms in 4 days,  how many people
are needed to paint 12 rooms in 6 days?
<pre>
3 people can paint 2 rooms in 4 days, so 
3 people can paint 6 rooms in 12 days. Therefore,
6 people can paint 12 rooms in 12 days, so
12 people can paint 12 rooms in 6 days.

ANSWER: 12 people

You can also use the worker-time-job formula, which is:

{{{(W[1]T[1])/J[1]}}}{{{""=""}}}{{{(W[2]T[2])/J[2]}}}

where

W<sub>1</sub> = the number of workers in the first situation.
T<sub>1</sub> = the number of time units (days in this case) in the first situation.
J<sub>1</sub> = the number of jobs in the first situation.

W<sub>2</sub> = the number of workers in the second situation.
T<sub>2</sub> = the number of time units (days in this case) in the second situation.
J<sub>2</sub> = the number of jobs in the second situation.

W<sub>1</sub> =  3             W<sub>2</sub> = the unknown quantity     
T<sub>1</sub> =  4             T<sub>2</sub> = 6 
J<sub>1</sub> =  2             J<sub>2</sub> = 12

{{{(W[1]*T[1])/J[1]}}}{{{""=""}}}{{{(W[2]*T[2])/J[2]}}}

{{{(3*4)/2}}}{{{""=""}}}{{{(W[2]*6)/12}}}

{{{12/2}}}{{{""=""}}}{{{(6*W[2])/12}}}

{{{12/2}}} reduces to {{{6}}} and {{{6*W[2]/12}}} reduces to {{{W[2]/2}}}

{{{6}}}{{{""=""}}}{{{(W[2])/2}}}

Multiply both sides by 2:

Answer = W<sub>2</sub> = 12 workers.  (or 'people').

Edwin</pre>