Answer:
Given the statement: It takes 54 minutes for 4 people to paint 6 walls [tex]\frac{54}{6} =9[/tex] minutes per wall
Since, it takes 4 people 9 minutes to paint 1 wall
Each person paints [tex]\frac{1}{4}[/tex] of the wall in 9 minutes
Each person paints [tex]\frac{1}{36}[/tex] of the wall in 1 minute at the same rate.
then;
6 people paint [tex]\frac{6}{36}[/tex] of 1 wall in 1 minute
⇒ Number of minutes it takes 6 people to paint 1 wall = 6 minutes
It takes 6 people 6 minutes to paint 1 wall
It takes 6 people [tex]6 \cdot 7 = 42[/tex] minutes to paint 7 walls
Therefore, it takes 42 minutes for 6 people to paint 7 walls.
The time is taken by the 6 people to paint 7 walls will be equal to 42 minutes.
In order to solve this we first have to calculate how long will it take one person to paint one wall:
[tex]\dfrac{54}{6}=9\ minutes[/tex]
That is between 4 people it will take 9 minutes to paint a wall, one person alone supposing they all work at the same rate will take 36 minutes.
Now we just multiply that by the number of walls to be painted:
[tex]36\times7=252[/tex]
And we divide that by the number of people painting:
[tex]\dfrac{252}{6}=42[/tex]
So it will take 42 minutes to paint 7 walls with 6 people painting.
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