We can paint 75 square feet of a surface every 45 minutes. We will determine how long it will take to paint a wall with the dimensions 7ft*6ft. Before we do so, we need to find the area of this wall. The wall is a rectangle. Let's plot it and label the dimensions.
Recall that when we want to find the area of a rectangle, we multiply its dimensions. Here, we need to multiply 7 feet by 6 feet.
7ft * 6ft = 42ft^2
Now, we will find the rate describing the relationship between the number of painted square feet and the number of minutes spent on painting. To do so, we will write a fraction. Later we will look for the amount of time it takes to paint 42 square feet. So, it will be easier if we put the number of minutes in the numerator, and the number of square feet in the denominator.
45minutes for 75square feet:45min/75ft^2
We can find the value of this rate. It will tell us how many minutes are needed to paint 1 square feet of a surface. To do so, we will divide the numerator and the denominator by the value from the denominator. This will leave us with 1 unit in the denominator.
45min/75ft^2=0.6min/1ft^2
Knowing the unit rate, we can find how much time it takes to paint 42 square feet of a surface. We will multiply the unit rate by 42 to do so.
