the number of hours to paint a house varies inversely with the number f painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. how many painters would you need to work in order to paint the house in 18 hours
We can solve this problem using the concept of inverse variation.
Let's assume the number of painters needed is represented by "p". According to the problem, the number of hours to paint the house, represented by "h", varies inversely with the number of painters working.
This can be written as: h = k/p, where k is the constant of variation.
We can use the information given in the problem to find the value of k.
When 6 painters are working, the house can be painted in 27 hours. Substituting these values into the equation:
27 = k/6
To find the value of k, we multiply both sides of the equation by 6:
27 * 6 = k
162 = k
Now we have the value of k, so we can rewrite the equation as:
h = 162/p
To find the number of painters needed to paint the house in 18 hours, we substitute h = 18 into the equation and solve for p:
18 = 162/p
To solve for p, we multiply both sides of the equation by p:
18p = 162
Then, we divide both sides of the equation by 18:
p = 162/18
p = 9
Therefore, you would need 9 painters to work in order to paint the house in 18 hours.