This is about direct variation.
The area a painter can paint varies directly with the amount of time he works. One morninig, he painted 204 ft² between 8 a.m. and 12:15 PM. Write a direct variation equation to describe the area y covered in x hours.
The forumlua for direct variation is y=kx
yes
To write a direct variation equation, we need to find the constant of variation, represented by 'k'.
In this case, we know that the area painted, 'y', varies directly with the amount of time worked, 'x' hours. We are also given specific values: at 8 a.m. to 12:15 PM, a total of 4 hours and 15 minutes was worked, and the area painted, 'y', was 204 ft².
First, let's convert the 12:15 PM time to decimal hours. There are 60 minutes in an hour, so 15 minutes is 15/60 = 0.25 hours. Therefore, the total time worked, 'x', is 4 hours + 0.25 hours = 4.25 hours.
Now we can write the direct variation equation, 'y = kx', using the known values:
204 = k * 4.25
To find the value of 'k', we divide both sides of the equation by 4.25:
k = 204 / 4.25
Calculating the value:
k ≈ 47.7647
So the direct variation equation for the area painted, 'y', in terms of the time worked, 'x', is:
y ≈ 47.7647x