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
Your data tells us that if x = 4.25, y = 204
sub into the equation
204 = 4.25kk = 204/4.25 = 48
so y = 48x
To write a direct variation equation to describe the area covered in x hours, we need to determine the constant of variation, k.
From the given information, we know that the painter painted 204 ft² between 8 a.m. and 12:15 PM, which is a total of 4 hours and 15 minutes. To convert the time into hours, we can divide the number of minutes by 60 and add it to the number of hours.
The equation to calculate the time in hours is:
x = 4 + (15/60) = 4.25 hours
Now, substitute the values into the formula for direct variation, y = kx:
204 = k * 4.25
To solve for k, divide both sides of the equation by 4.25:
k = 204 / 4.25
Calculating the value, k ≈ 48.
So, the direct variation equation to describe the area covered in x hours is:
y = 48x
This means that for every hour the painter works, the area covered will be 48 ft².