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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.

Ask by Simmons Reeves. in the United States
Jan 23,2025

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Tutor-Verified Answer

Answer

**Pinewoods Trail** is longer than **Outlook Trail**.

Solution

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**.

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Bonus Knowledge

To find out which trail is longer, we first need to convert the mixed numbers into improper fractions or decimal form for easier comparison. Lake Trail is \( 4 \frac{3}{5} = \frac{23}{5} \) miles or 4.6 miles. Outlook Trail is \( 5 \frac{5}{6} = \frac{35}{6} \) miles or approximately 5.83 miles. Pinewoods Trail is \( 1 \frac{3}{10} = \frac{13}{10} \) miles longer than Lake Trail, which gives us about 6.0 miles. Therefore, Pinewoods Trail, at approximately 6.0 miles, is longer than Outlook Trail at around 5.83 miles. When converting mixed numbers, remember to multiply the whole number by the denominator and then add the numerator. A common mistake is to miscalculate the fractions, so ensure that each step is double-checked! This careful attention to detail will help you avoid mistakes and arrive at the right conclusion.

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