Question

Two joggers run 6 miles south and then 5 miles east. What is the shortest distance they must travel to return to their starting point?

Answer 1

7.81 miles

The two joggers form a right triangle with the starting point as the right angle. They have run 6 miles south and 5 miles east, so the legs of the right triangle have lengths 6 and 5.

To find the shortest distance they must travel to return to their starting point, we need to find the length of the hypotenuse of the right triangle. We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the legs.

Plugging in the values we have, we get:

c^2 = 6^2 + 5^2
c^2 = 36 + 25
c^2 = 61

Taking the square root of both sides, we get:

c = sqrt(61)

Therefore, the shortest distance the joggers must travel to return to their starting point is approximately 7.81 miles.

Answer 2

The shortest distance the joggers must travel to return to their starting point is 7.81 miles.

To find the shortest distance the joggers must travel to return to their starting point, we can use the Pythagorean theorem, as the southward and eastward distances form a right triangle. The theorem states that the square of the length of the hypotenuse (the shortest distance, in this case) is equal to the sum of the squares of the other two sides:

a^2 + b^2 = c^2

Here, a is the southward distance (6 miles), and b is the eastward distance (5 miles). We need to find c, the hypotenuse.

(6 miles)^2 + (5 miles)^2 = c^2

36 + 25 = c^2

61 = c^2

Now, take the square root of both sides to find c:

c = √61

c ≈ 7.81 miles