MATH SOLVE

4 months ago

Q:
# 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

A:

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.

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.