Question

Two Viking ships leave the same place at the same time. One goes north 12 miles then east 6 miles. The other goes south 10 miles and west 7 miles. How far apart are they?

A) 35 miles
B) 26 miles
C) 20 miles
D) 17 miles

Answer 1

By applying the Pythagorean theorem to the paths of the two Viking ships, treating them as vectors, we find that the ships are approximately 26 miles apart after one travels north 12 miles and east 6 miles, and the other travels south 10 miles and west 7 miles. Therefore, the answer is B) 26 miles.

Step-by-step explanation:

To find how far apart the two Viking ships are after their respective journeys, we treat their paths as vectors and apply the Pythagorean theorem to calculate the distance between the end points of their travels. Ship A travels 12 miles north and then 6 miles east, while Ship B travels 10 miles south and then 7 miles west. The total distance Ship A has traveled north compared to Ship B is 12 (north) + 10 (south reversed direction) = 22 miles north. The total distance traveled east-west is 6 (east) + 7 (west) = 13 miles east. To find the straight-line distance between the two ships, we apply the Pythagorean theorem:

c^2 = a^2 + b^2

c^2 = 22^2 + 13^2

c^2 = 484 + 169

c^2 = 653

c = √653

c ≈ 25.55

The ships are approximately 26 miles apart, so the correct answer is B) 26 miles.