Understanding the Direction and Distance Puzzle

This problem involves tracking a person's movement through a series of turns and distances, starting from a bank and aiming for a hospital located east of the starting point. We need to determine the final direction and distance required to reach the hospital from Joya's final position.

Tracking Joya's Movements from the Bank

Let's assume the bank's location is the origin point (0,0) on a coordinate plane. North corresponds to the positive y-axis, South to the negative y-axis, East to the positive x-axis, and West to the negative x-axis.

We will track Joya's position after each step:

After all the movements, Joya is at the position (45, -22) relative to the bank.

Determining the Hospital's Location

The hospital is 45 m in east of the bank. Since the bank is at (0,0), the hospital's location is 45 units along the positive x-axis and 0 units along the y-axis.

Hospital Location: (45, 0)

Calculating the Final Move to Reach the Hospital

Joya is currently at (45, -22). She needs to reach the hospital at (45, 0).

Let's compare her current position (x_current, y_current) = (45, -22) with the hospital's position (x_hospital, y_hospital) = (45, 0).

• The x-coordinate is the same (45). This means she is already at the correct East/West position relative to the hospital.
• The y-coordinate needs to change from -22 to 0. This requires a movement in the positive y direction, which corresponds to North.

The distance she needs to walk is the difference in the y-coordinates:

Distance = \(|y_{\text{hospital}} - y_{\text{current}}|\)
Distance = \(|0 - (-22)|\)
Distance = \(|22|\)
Distance = 22 m

To move from (45, -22) to (45, 0), she needs to walk 22 m in the North direction.

Determining the Final Direction

Joya's last movement was East (Step 4). To move North from a position, she needs to turn relative to her last direction. If she was walking East, a Left turn takes her North, and a Right turn takes her South.

Since she needs to move North, she should turn Left from her current direction (East).

Summary of the Final Move

Joya is at (45, -22) and needs to reach (45, 0). She must move 22 m North. Her last movement was East. To move North from East, she needs to turn Left.

Therefore, she should turn Left and walk 22 m.

Comparing this with the given options, the correct answer is Left, 22 m.

Revision Table: Key Concepts

Additional Information: Solving Direction and Distance Problems

Direction and distance problems are common in reasoning sections of competitive exams. They test your ability to visualize movements and track positions.

Here are some tips for solving such problems:

• Always start from a reference point, often designated as the origin (0,0).
• Use a coordinate system to represent positions. North/South are along the y-axis, East/West along the x-axis.
• Keep track of the current direction after each turn. Remember:
• From North: Left is West, Right is East.
• From South: Left is East, Right is West.
• From East: Left is North, Right is South.
• From West: Left is South, Right is North.
• Draw a diagram if it helps visualize the path, but relying on coordinates is often more precise for complex movements.
• Break down the problem into steps, calculating the position after each movement.
• To find the final direction and distance between two points (current and target), calculate the difference in their x and y coordinates. This tells you the net displacement in the East/West and North/South directions.