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.

Question

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**.

Higher Order Thinking Lake Trail is
miles long. Outlook Trail is miles
long. Pinewoods Trail is miles longer
than Lake Trail. Which trail is longer,
Pinewoods Trail or Outlook Trail? Explain.

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Higher Order Thinking Lake Trail is miles long. Outlook Trail is miles long. Pinewoods Trail is miles longer than Lake Trail. Which trail is longer, Pinewoods Trail or Outlook Trail? Explain.