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 8 hours
Let's define the variables:
h = number of hours needed to paint the house
p = number of painters working
According to the problem, the number of hours (h) is inversely proportional to the number of painters (p). This can be written as h = k/p, where k is the constant of proportionality.
To find k, we can use the given information that a 2400-square foot house can be painted in 27 hours by 6 painters.
So, 27 = k/6.
Multiplying both sides by 6, we have k = 162.
Therefore, the equation relating the number of hours (h) and the number of painters (p) is h = 162/p.
Now we need to find out how many painters would be needed to paint the house in 8 hours.
Plugging in h = 8 into the equation, we get 8 = 162/p.
Rearranging the equation, we have p = 162/8 = 20.25.
Since we cannot have a fraction of a painter, we have to round up to the nearest whole number of painters.
Therefore, you would need 21 painters to work in order to paint the house in 8 hours.