It takes 636363 minutes for 444 people to paint 999 walls. how many minutes does it take 777 people to paint 444 walls? minutes

Accepted Solution

Let t=time, p=people, and w=walls.

We know that the time it takes is directly proportional to the length of the wall but inversely proportional to the number of people working. That is 
     [tex]t=k\cdot \frac{w}{p}[/tex]

We solve for the constant of proportionality, k.
     [tex]k=\frac{t\cdot p}{w}[/tex]

The initial values for k are the same for the final values. That is
     [tex]\frac{t_1\cdot p_1}{w_1}=\frac{t_2\cdot p_2}{w_2}[/tex]

     [tex]\frac{63\cdot 4}{9}=\frac{t_2\cdot 7}{4}[/tex]

     [tex]t_2=\frac{4\cdot 63\cdot 4}{7\cdot 9}=16[/tex]

It will take 16 minutes.