Calculate the amount of time a person has for this family within a span of 3 month, if he is working 9-10hrs for 5 days a week and rest for 8-10 hours and 2 hours in travelling.

To calculate the available time for family in a 3-month span, let's break down the given information and compute step by step.

### 1. Total Days and Hours in 3 Months
Assuming a 3-month period is approximately 90 days, we have:
\[
90 \text{ days} \times 24 \text{ hours} = 2160 \text{ hours}
\]

### 2. Weekly Work and Travel Time
- **Work time:** 9 to 10 hours per day for 5 days a week:
  \[
  9 \text{ hours} \times 5 = 45 \text{ hours/week (minimum)}
  \]
  \[
  10 \text{ hours} \times 5 = 50 \text{ hours/week (maximum)}
  \]
  
- **Travel time:** 2 hours daily for 5 days:
  \[
  2 \text{ hours} \times 5 = 10 \text{ hours/week}
  \]
  
Thus, total work + travel time per week ranges from:
  \[
  45 + 10 = 55 \text{ hours (minimum)}
  \]
  \[
  50 + 10 = 60 \text{ hours (maximum)}
  \]

### 3. Weekly Rest Time
If the person sleeps 8 to 10 hours daily:
  \[
  8 \text{ hours} \times 7 = 56 \text{ hours/week (minimum)}
  \]
  \[
  10 \text{ hours} \times 7 = 70 \text{ hours/week (maximum)}
  \]

### 4. Total Time for 3 Months
- **Weeks in 3 months:** \( \approx 12 \)
- Total work + travel time for 3 months:
  \[
  12 \times 55 = 660 \text{ hours (minimum)}
  \]
  \[
  12 \times 60 = 720 \text{ hours (maximum)}
  \]
- Total rest time for 3 months:
  \[
  12 \times 56 = 672 \text{ hours (minimum)}
  \]
  \[
  12 \times 70 = 840 \text{ hours (maximum)}
  \]

### 5. Available Family Time
Using the totals above, we find the family time by subtracting work, travel, and rest time from the 3-month period:

\[
2160 - (660 + 672) = 828 \text{ hours (maximum)}
\]
\[
2160 - (720 + 840) = 600 \text{ hours (minimum)}
\]

### Conclusion
In a 3-month span, the person has between **600 and 828 hours** available for family time.

Would you like more detailed steps on any part? 

---

1. What would the family time be if the person worked 6 days per week?
2. How much family time would be available if travel time increased to 3 hours per day?
3. What if the person reduced rest to 7 hours daily?
4. How does family time change if the workday is shortened to 8 hours?
5. What impact would a 4-day workweek have on family time?

**Tip:** Tracking daily time spent on various activities can help optimize for more family time.

Calculate the amount of time a person has for their family within a span of 3 months, if they are working 9-10 hours for 5 days a week, resting for 8-10 hours daily, and spending 2 hours commuting.

Discover how to calculate family time over a 3-month span when working 9-10 hours per day for 5 days a week, resting 8-10 hours daily, and spending 2 hours commuting. This problem uses basic arithmetic and time management concepts to balance work and personal time. Suitable for Grades 6-8.

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