**It took Meng 3 2/3 hours to get from Sacramento to Boston. Then it took Meng another 7 3/4 hours to get from Boston to Nashville. How long did Meng travel in total?**

To find the total time Meng traveled, we need to add the two time durations:

- Time from Sacramento to Boston: \(3 \frac{2}{3}\) hours
- Time from Boston to Nashville: \(7 \frac{3}{4}\) hours

### Step 1: Convert mixed numbers to improper fractions
- \(3 \frac{2}{3}\) as an improper fraction:
  \[
  3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}
  \]

- \(7 \frac{3}{4}\) as an improper fraction:
  \[
  7 \frac{3}{4} = \frac{7 \times 4 + 3}{4} = \frac{28 + 3}{4} = \frac{31}{4}
  \]

### Step 2: Find the common denominator and add the fractions
- The common denominator of 3 and 4 is 12.

- Convert \(\frac{11}{3}\) to have a denominator of 12:
  \[
  \frac{11}{3} = \frac{11 \times 4}{3 \times 4} = \frac{44}{12}
  \]

- Convert \(\frac{31}{4}\) to have a denominator of 12:
  \[
  \frac{31}{4} = \frac{31 \times 3}{4 \times 3} = \frac{93}{12}
  \]

- Now add the two fractions:
  \[
  \frac{44}{12} + \frac{93}{12} = \frac{44 + 93}{12} = \frac{137}{12}
  \]

### Step 3: Convert the improper fraction back to a mixed number
- Divide 137 by 12:
  \[
  137 \div 12 = 11 \text{ remainder } 5
  \]
  So, \(\frac{137}{12} = 11 \frac{5}{12}\).

### Final Answer:
Meng traveled a total of \(11 \frac{5}{12}\) hours.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you convert \(11 \frac{5}{12}\) hours into minutes?
2. If Meng had traveled 2 hours less, what would the total travel time have been?
3. How would the total travel time change if the trip from Boston to Nashville took 1 hour more?
4. What is the decimal form of the total travel time \(11 \frac{5}{12}\)?
5. How long would Meng's travel time be in seconds?

**Tip:** When adding mixed numbers, it can be helpful to first convert them into improper fractions to make the addition process smoother.

Learn how to calculate Meng's total travel time from Sacramento to Boston and then from Boston to Nashville. This problem involves adding mixed numbers and converting improper fractions. Suitable for students in Grades 4-6.

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