Question

The area a painter can paint varies directly with the amount of time he works. One morning, he painted 200ft2 between 8:00 a.m. and 1:00 p.m. Write a direct variation equation to describe the area y covered in x hours

Answer 1

The direct variation equation that describes the area y covered in x hours, where a painter can cover 200 square feet in 5 hours, is y = 40x. This equation indicates that the painter covers 40 square feet per every hour of work.

Step-by-step explanation:

The area a painter can paint varies directly with the amount of time he works, which is a situation that can be described by a direct variation equation. To establish this equation, we know that the painter covered 200 square feet in the time from 8:00 a.m. to 1:00 p.m., which is a duration of 5 hours. Therefore, the rate of painting is 200 ft2 per 5 hours or 40 ft2 per hour.

The direct variation equation that relates the area y covered in x hours can be written as:

y = kx

Where k is the constant of variation. In this case, since the painter paints 40 ft2 per hour, the equation becomes y = 40x.