In a city grid, each block on the east-west streets is 180 meters long. Each block on the north-south streets is also 180 meters long. A walker walks 4 blocks north and then 3 blocks east. How much farther did the walker travel than the actual distance between the start and end points?
distance as the crow flies=180*sqrt(4^2+3^2)
distance he walked: 180*(3+4)
To find the actual distance between the start and end points, we can use the Pythagorean theorem since the walker moves in a right-angled triangle pattern. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the walker moves 4 blocks north and 3 blocks east, forming a right triangle. The distance traveled north is the vertical leg, and the distance traveled east is the horizontal leg. We can consider each block as a unit of distance, so the vertical leg is 4 blocks and the horizontal leg is 3 blocks.
Using the Pythagorean theorem, we can calculate the hypotenuse, which represents the actual distance between the start and end points. Let's call the hypotenuse "d":
d² = (vertical leg)² + (horizontal leg)²
d² = (4 blocks)² + (3 blocks)²
d² = 16 + 9
d² = 25
Now, to find the actual distance, we take the square root of both sides:
d = √25
d = 5 blocks
Therefore, the actual distance between the start and end points is 5 blocks.
To find how much farther the walker traveled than the actual distance, we subtract the actual distance from the distance traveled. The distance traveled is the sum of the vertical and horizontal legs, which is 7 blocks (4 blocks north + 3 blocks east).
Difference = Distance traveled - Actual distance
Difference = 7 blocks - 5 blocks
Difference = 2 blocks
Therefore, the walker traveled 2 blocks farther than the actual distance between the start and end points.