Math Problem Statement

A boy runs 4 km to the East side then turns to the right side 6 km, and then turns left runs 8 km again. Turn left to run 3 km again, turn left 4 km, then turn right 1 km. Now the boy is in which direction?

Solution

Let's break down the boy's movements step by step and determine his final position and direction:

  1. First Movement: The boy runs 4 km to the East.
  2. Second Movement: The boy turns right (which is towards the South) and runs 6 km.
  3. Third Movement: The boy turns left (which is towards the East again) and runs 8 km.
  4. Fourth Movement: The boy turns left (which is now towards the North) and runs 3 km.
  5. Fifth Movement: The boy turns left (which is towards the West) and runs 4 km.
  6. Sixth Movement: The boy turns right (which is towards the North) and runs 1 km.

Final Direction:

After these steps, the boy is now facing North.

Would you like a detailed breakdown of his final position or any other clarification?

Here are 5 related questions to expand your understanding:

  1. How would the boy's final position change if he turned right instead of left on his third turn?
  2. What would the total distance traveled by the boy be?
  3. How could you represent this motion on a coordinate plane?
  4. What if the boy turned left after every move; where would he end up?
  5. How would this problem change if the directions were given as bearings (angles)?

Tip: Always keep track of direction changes as turning left or right alters relative orientation.

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Math Problem Analysis

Mathematical Concepts

Geometry
Direction and Movement
Coordinate System

Formulas

-

Theorems

Pythagorean Theorem (optional if discussing distance)
Right-hand rule for turns and direction

Suitable Grade Level

Grades 6-8