Grant is painting a rectangular board that has a width of 1/3 foot. He has enough paint to cover 3 square feet. If he is able to cover the whole board using all of his paint, what is the length of the board in feet?
The correct answer and explanation is:
To find the length of the board, we can use the formula for the area of a rectangle: Area=Length×Width\text{Area} = \text{Length} \times \text{Width}
Step 1: Plug in known values
We are told:
- The width of the board is 13\frac{1}{3} foot.
- Grant uses 3 square feet of paint, which means the area of the board is 3 square feet.
3=Length×133 = \text{Length} \times \frac{1}{3}
Step 2: Solve for length
To isolate the length, multiply both sides of the equation by 3: 3×3=Length3 \times 3 = \text{Length} Length=9\text{Length} = 9
✅ Final Answer: 9 feet
📘 Explanation (300 words)
This problem is about understanding how area works for a rectangle. The area of a rectangle is found by multiplying the length and the width. We are given that the width of the rectangular board is 13\frac{1}{3} foot, and the area is 3 square feet because that’s how much surface Grant can paint.
Our goal is to figure out the length of the board, which we’ll call LL. Using the area formula: Area=Length×Width\text{Area} = \text{Length} \times \text{Width}
we substitute the known values: 3=L×133 = L \times \frac{1}{3}
This is a simple equation where you need to solve for LL. To eliminate the fraction, multiply both sides by 3: 3×3=L3 \times 3 = L L=9L = 9
That means the board must be 9 feet long to have an area of 3 square feet with a width of 13\frac{1}{3} foot.
You can check the answer by multiplying: Length×Width=9×13=3 square feet\text{Length} \times \text{Width} = 9 \times \frac{1}{3} = 3 \text{ square feet}
Since this matches the amount of paint Grant has, the solution is correct. This type of problem helps reinforce understanding of how dimensions relate to area, especially when fractions are involved.