Question

Two people were walking in opposite directions. Both of them walked 6 miles forward then took right and walked 8 miles. How far is each from starting positions?

• A. 14 miles and 14 miles
• B. 10 miles and 10 miles
• C. 6 miles and 6 miles
• D. 12 miles and 12 miles

Answer 1

The Correct Option is B

To determine how far each person is from their starting position, we need to analyze their paths. Each person first walked 6 miles in one direction and then took a right turn, walking an additional 8 miles. This path forms a right triangle with the legs measuring 6 miles and 8 miles. We will use the Pythagorean theorem to find the distance from the starting point to the endpoint, which is the hypotenuse of the triangle.

The Pythagorean theorem states: 

a² + b² = c²

where a and b are the legs of the triangle, and c is the hypotenuse. Here, a = 6 miles and b = 8 miles. Plugging in these values, we have:

6² + 8² = c²

36 + 64 = c²

100 = c²

Taking the square root of both sides, we find:

c = √100 = 10 miles

Therefore, each person is 10 miles from their starting position after the described movements. The correct answer is 10 miles and 10 miles.