Zari and Taye both run approximately 8.48 miles on their training journeys.
1. Find Zari's path:
Start at point A, which is at (0, 0).
Run 2 miles north to point B, which is at (0, 2).
Run 4 miles east to point C, which is at (4, 2).
Run back to point A by going 4 miles west and 2 miles south.
2. Find Taye's path:
Start at point A', which is at (-5, -5).
Run 2 miles west to point B', which is at (-7, -5).
Run 4 miles south to point C', which is at (-7, -9).
Run back to point A' by going 4 miles east and 2 miles north.
3. Calculate the distances:
Zari's path is made up of three segments: AB, BC, and CA.
AB has a length of 2 miles (vertical).
BC has a length of 4 miles (horizontal).
CA has a length of 2√2 miles (hypotenuse of a right triangle with legs 2 and 4).
Using the Pythagorean theorem, we can find that the total distance Zari runs is AB + BC + CA = 2 + 4 + 2√2 ≈ 8.48 miles.
Taye's path is also made up of three segments: A'B', B'C', and C'A'. A'B' has a length of 2 miles (vertical).
B'C' has a length of 4 miles (horizontal).
C'A' has a length of 2√2 miles (hypotenuse of a right triangle with legs 2 and 4).
Taye's total distance is also AB' + B'C' + C'A' = 2 + 4 + 2√2 ≈ 8.48 miles.
Therefore, both Zari and Taye run approximately 8.48 miles on their training runs.