A carpenter spent a 40-hour workweek as follows:  of the time ordering materials;  of the time doing the woodwork; and of the time talking to customers. The rest of the time was devoted to cleanup. What is the approximate percentage of time the carpenter spent doing cleanup?

To determine the approximate percentage of time the carpenter spent on cleanup, we need to follow these steps:

1. **Identify the time spent on each task:**
   - Let \( x \) be the fraction of time spent on cleanup.
   - The time spent ordering materials, doing woodwork, and talking to customers are given as fractions. Suppose these fractions are \( \frac{1}{5} \), \( \frac{1}{2} \), and \( \frac{1}{10} \) respectively.

2. **Calculate the total time spent on tasks other than cleanup:**
   \[
   \text{Total time spent} = \frac{1}{5} + \frac{1}{2} + \frac{1}{10}
   \]
   To add these fractions, find a common denominator:
   \[
   \text{Common denominator} = 10
   \]
   Convert each fraction:
   \[
   \frac{1}{5} = \frac{2}{10}, \quad \frac{1}{2} = \frac{5}{10}, \quad \frac{1}{10} = \frac{1}{10}
   \]
   Now, add them:
   \[
   \frac{2}{10} + \frac{5}{10} + \frac{1}{10} = \frac{8}{10} = \frac{4}{5}
   \]

3. **Determine the fraction of time spent on cleanup:**
   The total workweek is 1 (or 100% of the time), so the fraction of time spent on cleanup is:
   \[
   1 - \frac{4}{5} = \frac{1}{5}
   \]

4. **Convert the fraction to a percentage:**
   Multiply the fraction by 100 to get the percentage:
   \[
   \frac{1}{5} \times 100 = 20\%
   \]

Thus, the carpenter spent **20%** of the time doing cleanup.

Would you like further details or have any other questions?

Here are some related questions to explore:

1. How much time did the carpenter spend ordering materials in hours?
2. What percentage of the workweek was spent talking to customers?
3. How many hours were dedicated to doing woodwork?
4. If the workweek was 50 hours instead of 40, how would the cleanup time change?
5. How would the percentages change if the time spent on woodwork increased?
6. What percentage of time was spent on all activities except cleanup?
7. How would the cleanup percentage change if the carpenter spent \( \frac{1}{4} \) of the time doing woodwork?
8. How can time management be optimized in a similar scenario?

**Tip:** Converting time fractions into percentages can provide a clearer understanding of how time is allocated across different tasks.

Learn how to calculate the approximate percentage of time a carpenter spends on cleanup in a 40-hour workweek. This problem involves fraction and percentage calculations, detailing the time allocated to ordering materials, doing woodwork, talking to customers, and cleanup.

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