From her home, Camille would have to walk 5 miles north to get to her friend Justine's house and 3 miles east to get to her friend Bryan's house. One day, Camille walked from her h... From her home, Camille would have to walk 5 miles north to get to her friend Justine's house and 3 miles east to get to her friend Bryan's house. One day, Camille walked from her home to Bryan's house. Together, Bryan and Camille cut directly through the field that separated them from Justine's house. When they finished playing at Justine's, Camille walked back home. In all, how far did Camille walk? If necessary, round to the nearest tenth. Read more

Steps to Solve

1. Determine the distance from home to Bryan's house

Camille walks 3 miles east from her home to reach Bryan's house.

2. Calculate the distance from Bryan's house to Justine's house

Using the Pythagorean theorem, we can find the direct distance from Bryan's house to Justine's house. The triangle formed has:

• One side = 5 miles (north to Justine's house)
• Other side = 3 miles (east to Bryan's house)

This is calculated as follows:

$$ d = \sqrt{(3^2 + 5^2)} $$

3. Calculate the direct distance from Bryan's house to Justine's house

Substituting in the values:

$$ d = \sqrt{(3^2 + 5^2)} = \sqrt{(9 + 25)} = \sqrt{34} $$

Calculating the square root:

$$ \sqrt{34} \approx 5.83 $$

4. Determine the distance from Justine's house back to Camille's home

Camille walked back from Justine's house to her home, which is the same distance as walking from home to Justine's house, so it’s 5 miles.

5. Total distance walked by Camille

Now, add all distances:

• Home to Bryan's house: 3 miles
• Bryan's house to Justine's house: approximately 5.83 miles
• Justine's house back to Camille's home: 5 miles

The total distance is:

$$ \text{Total distance} = 3 + 5.83 + 5 $$

Calculating the total distance:

$$ \text{Total distance} \approx 13.83 $$

6. Round to the nearest tenth

Rounding 13.83 to the nearest tenth gives us 13.8 miles.