Question

From her home, Helen would have to walk 7.8 kilometers north to get to her friend Toby's house and 4 kilometers east to get to her friend Candice's house. One day, Helen walked from her home to Candice's house. Together, Candice and Helen cut directly through the field that separated them from Toby's house. When they finished playing at Toby's, Helen walked back home. In all, how far did Helen walk? If necessary, round to the nearest tenth.

Answer 1

Helen walked a total distance of 20.6 kilometers after taking a route from her house to Candice's, then directly to Toby's, and finally back home.

Step-by-step explanation:

Helen initially walked from her home to Candice's house, which is 4 kilometers east. Together, they cut directly through a field to Toby's house, which is 7.8 kilometers north of Helen's house. Using the Pythagorean theorem, the distance directly from Candice's to Toby's house can be found. Since Helen's journey to Toby's is the hypotenuse of a right triangle with the other two sides being 7.8 km and 4 km, the direct distance (hypotenuse) can be calculated as:

Distance2 = 7.82 + 42

Distance2 = 60.84 + 16

Distance2 = 76.84

Distance ≈ √76.84

Distance ≈ 8.8 kilometers (rounded to the nearest tenth).

After spending time at Toby's, Helen walks directly back home, which is again 7.8 kilometers to the south. Therefore, the total distance Helen walked is:

Total distance = 4 km (to Candice's) + 8.8 km (to Toby's) + 7.8 km (back home) = 20.6 kilometers.