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?
- 14 miles and 14 miles
- 10 miles and 10 miles
- 6 miles and 6 miles
- 12 miles and 12 miles
The Correct Option is B
Solution and Explanation
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.
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