In a city grid, each block on the east-west streets is 100 meters long. Each block on the north-south streets is 20 meters long. A walker walks 4 blocks west and then 4 blocks south. How much father did the walker travel than the actual distance between the start and end points?
A) 79m
B) 80m
C) 60m
D) 72m
E) 66m
D)
{4•100 +4•80} – sqrt(400² +80²) = 72 m
To find the actual distance between the start and end points, we can use the Pythagorean theorem.
The distance traveled horizontally (west) is 4 blocks, and each block is 100 meters long. So the horizontal distance traveled is 4 * 100 = 400 meters.
The distance traveled vertically (south) is 4 blocks, and each block is 20 meters long. So the vertical distance traveled is 4 * 20 = 80 meters.
Using the Pythagorean theorem, we can calculate the actual distance between the start and end points:
Actual distance = √(horizontal distance^2 + vertical distance^2)
Actual distance = √(400^2 + 80^2)
Actual distance = √(160000 + 6400)
Actual distance = √166400
Actual distance ≈ 407.15 meters
The distance the walker actually traveled is the sum of the horizontal and vertical distances: 400 meters + 80 meters = 480 meters.
Therefore, the walker traveled 480 - 407.15 ≈ **72.85 meters** farther than the actual distance between the start and end points.
The answer is not listed in the options provided.
To solve this problem, we need to calculate the distance the walker traveled and subtract it from the actual distance between the start and end points.
The walker first walks 4 blocks west. Since each east-west block is 100 meters long, this means the walker traveled a distance of 4 blocks * 100 meters/block = 400 meters west.
The walker then walks 4 blocks south. Since each north-south block is 20 meters long, this means the walker traveled a distance of 4 blocks * 20 meters/block = 80 meters south.
Now we can calculate the actual distance between the start and end points of the walker's journey.
The horizontal displacement (west) is 400 meters. Since the walker didn't move north or south, the vertical displacement is 0 meters. Therefore, the actual distance between the start and end points is the hypotenuse of a right triangle with the horizontal and vertical displacements as its sides.
Using the Pythagorean theorem, we can calculate the actual distance:
actual_distance = √[ (400 meters)^2 + (0 meters)^2 ]
actual_distance = √[ 160,000 meters^2 + 0 meters^2 ]
actual_distance = √160,000 meters^2
actual_distance = 400 meters
Now we can calculate the difference between the distance the walker traveled and the actual distance:
difference = (400 meters + 80 meters) - 400 meters
difference = 480 meters - 400 meters
difference = 80 meters
Therefore, the walker traveled 80 meters farther than the actual distance between the start and end points.
Thus, the answer is B) 80m.