4. Two joggers run 8 miles north and then 5 miles west. What is the shortest distance they must travel to return to their starting point?
Draw a picture:
Solve:
To find the shortest distance they must travel to return to their starting point, we can use the Pythagorean theorem since the joggers have run in two perpendicular directions.
Let's call the starting point O, the end point after running 8 miles north A, and the end point after running 5 miles west B.
From the given information, we can see that triangle OAB is a right triangle.
We can calculate the shortest distance by using the Pythagorean theorem:
AB^2 = OA^2 + OB^2
AB^2 = 8^2 + 5^2
AB^2 = 64 + 25
AB^2 = 89
AB ≈ √89 ≈ 9.43 miles
Therefore, the shortest distance the joggers must travel to return to their starting point is approximately 9.43 miles.