Final answer:
The quickest way back for Jackie from her starting point is approximately 2.69 miles.
Step-by-step explanation:
To find the quickest way back to her starting point, we need to find the shortest distance between her final position and the origin. This can be done by finding the distance between the starting point and the final position in a straight line.
Using the Pythagorean theorem, we can calculate this distance. The distance traveled west is 1 mile, and the distance traveled north is 2.5 miles. Therefore, the distance between the starting point and the final position is the hypotenuse of a right triangle with sides 1 mile and 2.5 miles.
Using the formula for the hypotenuse of a right triangle, we can calculate the distance as follows:
Distance = sqrt((1 mile)^2 + (2.5 miles)^2)
Distance = sqrt(1 + 6.25) miles
Distance = sqrt(7.25) miles
Distance ≈ 2.69 miles