4. Higher Order Thinking Lake Trail is $$ 4 \frac{3}{5} $$ miles long. Outlook Trail is $$ 5 \frac{5}{6} $$ miles long. Pinewoods Trail is $$ 1 \frac{3}{10} $$ miles longer than Lake Trail. Which trail is longer, Pinewoods Trail or Outlook Trail? Explain.

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UpStudy AI · Accepted Answer

To determine which trail is longer—**Pinewoods Trail** or **Outlook Trail**—let's break down the given information and perform the necessary calculations.

### Given:
1. **Lake Trail** is $$ 4 \frac{3}{5} $$ miles long.
2. **Outlook Trail** is $$ 5 \frac{5}{6} $$ miles long.
3. **Pinewoods Trail** is $$ 1 \frac{3}{10} $$ miles longer than Lake Trail.

### Step 1: Calculate the Length of Pinewoods Trail

First, we need to find out how long the Pinewoods Trail is by adding the additional distance to the Lake Trail.

$$
\text{Lake Trail} = 4 \frac{3}{5} \text{ miles} = \frac{23}{5} \text{ miles}
$$
$$
\text{Additional Distance} = 1 \frac{3}{10} \text{ miles} = \frac{13}{10} \text{ miles}
$$
$$
\text{Pinewoods Trail} = \text{Lake Trail} + \text{Additional Distance} = \frac{23}{5} + \frac{13}{10}
$$

To add these fractions, they need a common denominator. The least common denominator (LCD) of 5 and 10 is 10.

$$
\frac{23}{5} = \frac{46}{10}
$$
$$
\frac{46}{10} + \frac{13}{10} = \frac{59}{10} = 5 \frac{9}{10} \text{ miles}
$$

So, **Pinewoods Trail** is $$ 5 \frac{9}{10} $$ miles long.

### Step 2: Compare Pinewoods Trail with Outlook Trail

Now, let's compare the lengths of Pinewoods Trail and Outlook Trail.

$$
\text{Outlook Trail} = 5 \frac{5}{6} \text{ miles} = \frac{35}{6} \text{ miles}
$$
$$
\text{Pinewoods Trail} = 5 \frac{9}{10} \text{ miles} = \frac{59}{10} \text{ miles}
$$

To compare these, it's helpful to convert them to decimals or to have a common denominator.

**Converting to Decimals:**
$$
\frac{35}{6} \approx 5.833 \text{ miles}
$$
$$
\frac{59}{10} = 5.9 \text{ miles}
$$

**Conclusion:**
$$
5.9 \text{ miles} > 5.833 \text{ miles}
$$

Therefore, **Pinewoods Trail** ($$ 5 \frac{9}{10} $$ miles) is **longer** than **Outlook Trail** ($$ 5 \frac{5}{6} $$ miles).

### Summary:

- **Pinewoods Trail:** $$ 5 \frac{9}{10} $$ miles
- **Outlook Trail:** $$ 5 \frac{5}{6} $$ miles

Since $$ 5 \frac{9}{10} > 5 \frac{5}{6} $$, **Pinewoods Trail** is longer than **Outlook Trail**.
**Pinewoods Trail** is longer than **Outlook Trail**.

4. Higher Order Thinking Lake Trail is \( 4 \frac{3}{5} \) miles long. Outlook Trail is \( 5 \frac{5}{6} \) miles long. Pinewoods Trail is \( 1 \frac{3}{10} \) miles longer than Lake Trail. Which trail is longer, Pinewoods Trail or Outlook Trail? Explain.

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