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

Step 1: Understanding the Concept.
Each person's path forms two straight legs at a right angle to each other (walk forward, then turn right), so the direct distance back to the start is the hypotenuse of a right triangle.

Step 2: Apply the Pythagorean theorem.
For either person, distance from start \(=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\) miles.

Step 3: Note this is the same for both.
Even though the two people walk in opposite overall directions, each one individually turns through the same right angle after the same 6-mile leg and the same 8-mile leg, so both end up exactly 10 miles from their own starting point.

Step 4: Final Answer.
Both are 10 miles from their starting point, so option B is correct.