Final answer:
Ranell's training route forms a right triangle, and the Pythagorean theorem is used to find the straight-line distance home. Multiply the total daily distance by 5 to get the total distance over 5 days: 60 miles.
Step-by-step explanation:
Ranell runs a two-dimensional path consisting of a 3-mile eastward run followed by a 4-mile northward run. The straight-line distance back to his house can be determined by the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
To find the straight-line distance home, we calculate the hypotenuse (c) of the right triangle formed by his east and north runs:
c = √(3² + 4²) = √(9 + 16) = √25 = 5 miles
The total distance Ranell runs in one day is the sum of the distances he runs east, north, and the straight-line distance home, which is 3 + 4 + 5 = 12 miles. To find the total distance over 5 days, we multiply 12 miles by 5:
Total distance over 5 days = 12 miles/day × 5 days = 60 miles
Therefore, the total distance Ranell will run after 5 days of training is 60 miles.