How many hours will it take Leah to paint the entire fence?

Understand the Problem

The question is asking how long it will take Leah to paint her entire garden fence based on the time it takes her to paint a fraction of it. We need to calculate the total time based on the unit rates provided in the options.

Answer

Leah will take \( 6 \) hours to paint her entire garden fence.

Steps to Solve

Calculate the Rate of Work Leah paints ( \frac{1}{36} ) of her fence in ( \frac{1}{6} ) of an hour. To find out how much time it takes her to paint 1 part of the fence, we can find her painting rate:

[ \text{Rate} = \frac{\text{Time}}{\text{Fraction of fence}} = \frac{\frac{1}{6}}{\frac{1}{36}} = \frac{1}{6} \times \frac{36}{1} = 6 \text{ hours for the entire fence.} ]

Determine Total Time to Paint Entire Fence Since we found that it takes Leah 6 hours to paint the entire garden fence, we can use this information to answer the question.
Identify how to use the existing information From the previous step, we can see that the total time can be expressed as:

[ \text{Total Time} = \text{Time per 1 part} \times \text{Number of parts} ]

Given that the entire fence represents 36 parts (as ( \frac{1}{36} ) is one of those parts), she requires ( 6 ) hours total.

Leah will take a total of ( 6 ) hours to paint her entire garden fence.

More Information

This calculation is useful in various practical scenarios. Understanding unit rates can help in estimating time or resource requirements in tasks such as painting, building, or any similar project.

Tips

Miscalculating the rate: A common mistake is to forget to convert fractions correctly when calculating unit rates. Always ensure that when you are calculating rates or ratios, the units are consistent and fractions are simplified correctly.
Ignoring the total parts: It can be easy to overlook the overall number of parts when calculating total time from unit time.

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