Final answer:
To determine the time needed to paint 500 feet of fence, we set up a proportion based on the given information that 5 hours is needed for 200 feet. Solving this proportion, we find that it will take 12.5 hours to paint 500 feet of fence.
Step-by-step explanation:
The time needed to paint a fence varies directly with the length of the fence, meaning the time required to paint the fence is proportional to its length. Given that it takes 5 hours to paint 200 feet, we can set up a proportion to find out how long it will take to paint 500 feet of fence. We can write this relationship as:
Time (in hours) / Length (in feet) = Constant rate of work
So for the given problem:
5 hours / 200 feet = x hours / 500 feet
Now we solve for x, which is the time it will take to paint 500 feet:
- Multiply both sides by 500 feet to isolate x on one side of the equation:
- (5 hours / 200 feet) * 500 feet = x
- Simplify the equation:
- (5 * 500) / 200 = x
- Calculate the result:
- 2500 / 200 = x
- 12.5 = x
Therefore, it will take 12.5 hours to paint 500 feet of fence.