Question

Two people were walking in opposite directions from the same starting point. Both of them walked 6 miles forward, then took a right turn and walked 8 miles. How far is each of them from their starting position?

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

Hint:

6 and 8 are the legs of a right triangle; recognise the 6-8-10 Pythagorean triple.

Answer 1

The Correct Option is B

Since the two legs of each person's walk (6 miles, then 8 miles after a right turn) are perpendicular to each other, this is really just a right-triangle distance problem repeated twice.

1. Recognise the 6, 8 legs as the two perpendicular sides of a right triangle, with the straight-line distance back to start as the hypotenuse.
2. Notice that $6, 8, 10$ is a Pythagorean triple ($6^2+8^2=36+64=100=10^2$), so the hypotenuse is exactly 10 without needing a calculator.
3. Since both people follow the identical pattern of moves (just mirrored in overall direction), the same 10-mile result applies to each of them independently.

So the correct answer is option B, 10 miles and 10 miles.